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Extensions 1→N→G→Q→1 with N=S3×C2×C6 and Q=C6

Direct product G=N×Q with N=S3×C2×C6 and Q=C6
dρLabelID
S3×C2×C62144S3xC2xC6^2432,772

Semidirect products G=N:Q with N=S3×C2×C6 and Q=C6
extensionφ:Q→Out NdρLabelID
(S3×C2×C6)⋊C6 = S32×A4φ: C6/C1 → C6 ⊆ Out S3×C2×C62412+(S3xC2xC6):C6432,749
(S3×C2×C6)⋊2C6 = S3×C6×A4φ: C6/C2 → C3 ⊆ Out S3×C2×C6366(S3xC2xC6):2C6432,763
(S3×C2×C6)⋊3C6 = C6×D6⋊S3φ: C6/C3 → C2 ⊆ Out S3×C2×C648(S3xC2xC6):3C6432,655
(S3×C2×C6)⋊4C6 = C6×C3⋊D12φ: C6/C3 → C2 ⊆ Out S3×C2×C648(S3xC2xC6):4C6432,656
(S3×C2×C6)⋊5C6 = C3×S3×C3⋊D4φ: C6/C3 → C2 ⊆ Out S3×C2×C6244(S3xC2xC6):5C6432,658
(S3×C2×C6)⋊6C6 = C3×C6×D12φ: C6/C3 → C2 ⊆ Out S3×C2×C6144(S3xC2xC6):6C6432,702
(S3×C2×C6)⋊7C6 = S3×D4×C32φ: C6/C3 → C2 ⊆ Out S3×C2×C672(S3xC2xC6):7C6432,704
(S3×C2×C6)⋊8C6 = C3×C6×C3⋊D4φ: C6/C3 → C2 ⊆ Out S3×C2×C672(S3xC2xC6):8C6432,709
(S3×C2×C6)⋊9C6 = S32×C2×C6φ: C6/C3 → C2 ⊆ Out S3×C2×C648(S3xC2xC6):9C6432,767

Non-split extensions G=N.Q with N=S3×C2×C6 and Q=C6
extensionφ:Q→Out NdρLabelID
(S3×C2×C6).C6 = C2×S3×C3.A4φ: C6/C2 → C3 ⊆ Out S3×C2×C6366(S3xC2xC6).C6432,541
(S3×C2×C6).2C6 = C9×D6⋊C4φ: C6/C3 → C2 ⊆ Out S3×C2×C6144(S3xC2xC6).2C6432,135
(S3×C2×C6).3C6 = C18×D12φ: C6/C3 → C2 ⊆ Out S3×C2×C6144(S3xC2xC6).3C6432,346
(S3×C2×C6).4C6 = S3×D4×C9φ: C6/C3 → C2 ⊆ Out S3×C2×C6724(S3xC2xC6).4C6432,358
(S3×C2×C6).5C6 = C18×C3⋊D4φ: C6/C3 → C2 ⊆ Out S3×C2×C672(S3xC2xC6).5C6432,375
(S3×C2×C6).6C6 = C3×D6⋊Dic3φ: C6/C3 → C2 ⊆ Out S3×C2×C648(S3xC2xC6).6C6432,426
(S3×C2×C6).7C6 = C32×D6⋊C4φ: C6/C3 → C2 ⊆ Out S3×C2×C6144(S3xC2xC6).7C6432,474
(S3×C2×C6).8C6 = S3×C6×Dic3φ: C6/C3 → C2 ⊆ Out S3×C2×C648(S3xC2xC6).8C6432,651
(S3×C2×C6).9C6 = S3×C2×C36φ: trivial image144(S3xC2xC6).9C6432,345
(S3×C2×C6).10C6 = S3×C22×C18φ: trivial image144(S3xC2xC6).10C6432,557
(S3×C2×C6).11C6 = S3×C6×C12φ: trivial image144(S3xC2xC6).11C6432,701

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