Essential welded pairs: $S: BQ^6_{1} \quad U = ((2 3)(4 5) , (1 4)(3 6) , (1 5)(2 6) , (1 5)(2 6) , (1 4)(3 6) , (2 3)(4 5)) \quad D = ((2 5)(3 4) , \iota , \iota , (1 6)(2 5) , (1 6)(3 4) , \iota)$\hfil\break $T: Q^6_{72} \quad U = \iota \quad D = \iota$\hfil\break $S: BQ^6_{38} \quad U = ((2 3 5 6) , (1 4)(3 6) , (1 4)(2 5) , (2 6 5 3) , (1 4)(3 6) , (1 4)(2 5)) \quad D = ((2 5)(3 6) , \iota , \iota , (2 5)(3 6) , \iota , \iota)$\hfil\break $T: Q^6_{72} \quad U = \iota \quad D = \iota$\hfil\break $S: BQ^6_{43} \quad U = ((2 3)(5 6) , (1 4)(3 5) , (1 4)(2 6) , (2 5)(3 6) , (1 4)(2 6) , (1 4)(3 5)) \quad D = ((2 6)(3 5) , \iota , \iota , (2 6)(3 5) , \iota , \iota)$\hfil\break $T: Q^6_{72} \quad U = \iota \quad D = \iota$\hfil\break $S: BQ^6_{57} \quad U = ((3 4 5 6) , (3 4 5 6) , \iota , \iota , \iota , \iota) \quad D = ((3 5)(4 6) , \iota , (1 2)(4 6) , (1 2)(3 5) , (1 2)(4 6) , (1 2)(3 5))$\hfil\break $T: Q^6_{72} \quad U = \iota \quad D = \iota$\hfil\break $S: BQ^6_{66} \quad U = ((2 3 4)(5 6) , (1 4 3)(5 6) , (1 2 4)(5 6) , (1 3 2)(5 6) , \iota , \iota) \quad D = ((5 6) , (5 6) , (5 6) , (5 6) , \iota , \iota)$\hfil\break $T: Q^6_{72} \quad U = \iota \quad D = \iota$\hfil\break $S: BQ^6_{96} \quad U = ((2 3 4) , (1 4 3) , (1 2 4) , (1 3 2) , \iota , \iota) \quad D = ((5 6) , (5 6) , (5 6) , (5 6) , \iota , \iota)$\hfil\break $T: Q^6_{72} \quad U = \iota \quad D = \iota$\hfil\break $S: BQ^6_{119} \quad U = ((2 3)(4 5) , \iota , \iota , \iota , \iota , (2 3)(4 5)) \quad D = ((2 4)(3 5) , (1 6)(3 5) , (1 6)(2 4) , (1 6)(3 5) , (1 6)(2 4) , \iota)$\hfil\break $T: Q^6_{72} \quad U = \iota \quad D = \iota$\hfil\break $S: BQ^6_{481} \quad U = ((2 3)(4 5) , (1 3)(4 5) , (1 2)(4 5) , \iota , \iota , \iota) \quad D = (\iota , \iota , \iota , \iota , \iota , (4 5))$\hfil\break $T: BQ^6_{1503} \quad U = ((4 5) , (4 5) , (4 5) , \iota , \iota , (4 5)) \quad D = ((4 5) , (4 5) , (4 5) , \iota , \iota , (4 5))$\hfil\break $S: BQ^6_{481} \quad U = ((2 3)(4 5) , (1 3)(4 5) , (1 2)(4 5) , \iota , \iota , \iota) \quad D = (\iota , \iota , \iota , \iota , \iota , (4 5))$\hfil\break $T: Q^6_{72} \quad U = \iota \quad D = \iota$\hfil\break $S: BQ^6_{482} \quad U = ((2 3)(4 5) , (1 3)(4 5) , (1 2)(4 5) , \iota , \iota , \iota) \quad D = ((4 5) , (4 5) , (4 5) , \iota , \iota , \iota)$\hfil\break $T: BQ^6_{1503} \quad U = ((4 5) , (4 5) , (4 5) , \iota , \iota , (4 5)) \quad D = ((4 5) , (4 5) , (4 5) , \iota , \iota , (4 5))$\hfil\break $S: BQ^6_{482} \quad U = ((2 3)(4 5) , (1 3)(4 5) , (1 2)(4 5) , \iota , \iota , \iota) \quad D = ((4 5) , (4 5) , (4 5) , \iota , \iota , \iota)$\hfil\break $T: Q^6_{72} \quad U = \iota \quad D = \iota$\hfil\break $S: BQ^6_{483} \quad U = ((2 3)(4 5) , (1 3)(4 5) , (1 2)(4 5) , \iota , \iota , (4 5)) \quad D = (\iota , \iota , \iota , \iota , \iota , (4 5))$\hfil\break $T: BQ^6_{1503} \quad U = ((4 5) , (4 5) , (4 5) , \iota , \iota , (4 5)) \quad D = ((4 5) , (4 5) , (4 5) , \iota , \iota , (4 5))$\hfil\break $S: BQ^6_{483} \quad U = ((2 3)(4 5) , (1 3)(4 5) , (1 2)(4 5) , \iota , \iota , (4 5)) \quad D = (\iota , \iota , \iota , \iota , \iota , (4 5))$\hfil\break $T: Q^6_{72} \quad U = \iota \quad D = \iota$\hfil\break $S: BQ^6_{484} \quad U = ((2 3)(4 5) , (1 3)(4 5) , (1 2)(4 5) , \iota , \iota , (4 5)) \quad D = ((4 5) , (4 5) , (4 5) , \iota , \iota , \iota)$\hfil\break $T: BQ^6_{1503} \quad U = ((4 5) , (4 5) , (4 5) , \iota , \iota , (4 5)) \quad D = ((4 5) , (4 5) , (4 5) , \iota , \iota , (4 5))$\hfil\break $S: BQ^6_{484} \quad U = ((2 3)(4 5) , (1 3)(4 5) , (1 2)(4 5) , \iota , \iota , (4 5)) \quad D = ((4 5) , (4 5) , (4 5) , \iota , \iota , \iota)$\hfil\break $T: Q^6_{72} \quad U = \iota \quad D = \iota$\hfil\break $S: BQ^6_{585} \quad U = ((2 3) , (1 3) , (1 2) , \iota , (4 6) , \iota) \quad D = ((4 6) , (4 6) , (4 6) , \iota , \iota , \iota)$\hfil\break $T: Q^6_{72} \quad U = \iota \quad D = \iota$\hfil\break $S: BQ^6_{586} \quad U = ((2 3) , (1 3) , (1 2) , \iota , \iota , \iota) \quad D = ((4 5) , (4 5) , (4 5) , \iota , \iota , \iota)$\hfil\break $T: BQ^6_{1503} \quad U = ((4 5) , (4 5) , (4 5) , \iota , \iota , (4 5)) \quad D = ((4 5) , (4 5) , (4 5) , \iota , \iota , (4 5))$\hfil\break $S: BQ^6_{586} \quad U = ((2 3) , (1 3) , (1 2) , \iota , \iota , \iota) \quad D = ((4 5) , (4 5) , (4 5) , \iota , \iota , \iota)$\hfil\break $T: Q^6_{72} \quad U = \iota \quad D = \iota$\hfil\break $S: Q^6_{33} \quad U = ((2 3)(4 5 6) , (1 3)(4 5 6) , (1 2)(4 5 6) , \iota , \iota , \iota) \quad D = \iota$\hfil\break $T: BQ^6_{1204} \quad U = ((4 5 6) , (4 5 6) , (4 5 6) , \iota , \iota , \iota) \quad D = ((4 6 5) , (4 6 5) , (4 6 5) , \iota , \iota , \iota)$\hfil\break $S: Q^6_{67} \quad U = ((2 3) , (1 3) , (1 2) , \iota , \iota , \iota) \quad D = \iota$\hfil\break $T: BQ^6_{1204} \quad U = ((4 5 6) , (4 5 6) , (4 5 6) , \iota , \iota , \iota) \quad D = ((4 6 5) , (4 6 5) , (4 6 5) , \iota , \iota , \iota)$\hfil\break $S: Q^6_{35} \quad U = ((2 3)(4 5) , (1 3)(4 5) , (1 2)(4 5) , \iota , \iota , \iota) \quad D = \iota$\hfil\break $T: BQ^6_{1503} \quad U = ((4 5) , (4 5) , (4 5) , \iota , \iota , (4 5)) \quad D = ((4 5) , (4 5) , (4 5) , \iota , \iota , (4 5))$\hfil\break $S: Q^6_{36} \quad U = ((2 3)(4 5) , (1 3)(4 5) , (1 2)(4 5) , \iota , \iota , (4 5)) \quad D = \iota$\hfil\break $T: BQ^6_{1503} \quad U = ((4 5) , (4 5) , (4 5) , \iota , \iota , (4 5)) \quad D = ((4 5) , (4 5) , (4 5) , \iota , \iota , (4 5))$\hfil\break $S: Q^6_{67} \quad U = ((2 3) , (1 3) , (1 2) , \iota , \iota , \iota) \quad D = \iota$\hfil\break $T: BQ^6_{1503} \quad U = ((4 5) , (4 5) , (4 5) , \iota , \iota , (4 5)) \quad D = ((4 5) , (4 5) , (4 5) , \iota , \iota , (4 5))$\hfil\break $S: Q^6_{1} \quad U = ((2 3)(4 5) , (1 4)(3 6) , (1 5)(2 6) , (1 5)(2 6) , (1 4)(3 6) , (2 3)(4 5)) \quad D = \iota$\hfil\break $T: Q^6_{72} \quad U = \iota \quad D = \iota$\hfil\break $S: Q^6_{3} \quad U = ((2 3 5 6) , (1 4)(3 6) , (1 4)(2 5) , (2 6 5 3) , (1 4)(3 6) , (1 4)(2 5)) \quad D = \iota$\hfil\break $T: Q^6_{72} \quad U = \iota \quad D = \iota$\hfil\break $S: Q^6_{4} \quad U = ((2 4 5 3) , (1 3 6 4) , (1 5 6 2) , (1 2 6 5) , (1 4 6 3) , (2 3 5 4)) \quad D = \iota$\hfil\break $T: Q^6_{72} \quad U = \iota \quad D = \iota$\hfil\break $S: Q^6_{8} \quad U = ((2 3)(5 6) , (1 4)(3 5) , (1 4)(2 6) , (2 5)(3 6) , (1 4)(2 6) , (1 4)(3 5)) \quad D = \iota$\hfil\break $T: Q^6_{72} \quad U = \iota \quad D = \iota$\hfil\break $S: Q^6_{9} \quad U = ((2 3)(4 5) , (1 4)(3 5) , (1 5)(2 4) , (1 3)(2 5) , (1 2)(3 4) , \iota) \quad D = \iota$\hfil\break $T: Q^6_{72} \quad U = \iota \quad D = \iota$\hfil\break $S: Q^6_{10} \quad U = ((2 4 5 3) , (1 5 4 3) , (1 4 2 5) , (1 3 5 2) , (1 2 3 4) , \iota) \quad D = \iota$\hfil\break $T: Q^6_{72} \quad U = \iota \quad D = \iota$\hfil\break $S: Q^6_{20} \quad U = ((2 3 4)(5 6) , (1 4 3)(5 6) , (1 2 4)(5 6) , (1 3 2)(5 6) , \iota , \iota) \quad D = \iota$\hfil\break $T: Q^6_{72} \quad U = \iota \quad D = \iota$\hfil\break $S: Q^6_{22} \quad U = (\iota , (3 4 6) , (2 5)(4 6) , (2 5)(3 6) , (3 6 4) , (2 5)(3 4)) \quad D = \iota$\hfil\break $T: Q^6_{72} \quad U = \iota \quad D = \iota$\hfil\break $S: Q^6_{31} \quad U = ((2 3)(5 6) , (1 3)(4 5) , (1 2)(4 6) , \iota , \iota , \iota) \quad D = \iota$\hfil\break $T: Q^6_{72} \quad U = \iota \quad D = \iota$\hfil\break $S: Q^6_{32} \quad U = ((2 3)(5 6) , (1 3)(4 5) , (1 2)(4 6) , (2 5)(3 6) , (1 6)(2 4) , (1 5)(3 4)) \quad D = \iota$\hfil\break $T: Q^6_{72} \quad U = \iota \quad D = \iota$\hfil\break $S: Q^6_{33} \quad U = ((2 3)(4 5 6) , (1 3)(4 5 6) , (1 2)(4 5 6) , \iota , \iota , \iota) \quad D = \iota$\hfil\break $T: Q^6_{72} \quad U = \iota \quad D = \iota$\hfil\break $S: Q^6_{34} \quad U = ((2 3 4) , (1 4 3) , (1 2 4) , (1 3 2) , \iota , \iota) \quad D = \iota$\hfil\break $T: Q^6_{72} \quad U = \iota \quad D = \iota$\hfil\break $S: Q^6_{35} \quad U = ((2 3)(4 5) , (1 3)(4 5) , (1 2)(4 5) , \iota , \iota , \iota) \quad D = \iota$\hfil\break $T: Q^6_{72} \quad U = \iota \quad D = \iota$\hfil\break $S: Q^6_{36} \quad U = ((2 3)(4 5) , (1 3)(4 5) , (1 2)(4 5) , \iota , \iota , (4 5)) \quad D = \iota$\hfil\break $T: Q^6_{72} \quad U = \iota \quad D = \iota$\hfil\break $S: Q^6_{63} \quad U = ((2 3) , (1 3) , (1 2) , \iota , (4 6) , \iota) \quad D = \iota$\hfil\break $T: Q^6_{72} \quad U = \iota \quad D = \iota$\hfil\break $S: Q^6_{64} \quad U = ((2 3) , (1 3) , (1 2) , (5 6) , (4 6) , (4 5)) \quad D = \iota$\hfil\break $T: Q^6_{72} \quad U = \iota \quad D = \iota$\hfil\break $S: Q^6_{67} \quad U = ((2 3) , (1 3) , (1 2) , \iota , \iota , \iota) \quad D = \iota$\hfil\break $T: Q^6_{72} \quad U = \iota \quad D = \iota$\hfil\break