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

Direct product G=N×Q with N=S3×C2×C6 and Q=S3
dρLabelID
S32×C2×C648S3^2xC2xC6432,767

Semidirect products G=N:Q with N=S3×C2×C6 and Q=S3
extensionφ:Q→Out NdρLabelID
(S3×C2×C6)⋊1S3 = C3×S3×S4φ: S3/C1 → S3 ⊆ Out S3×C2×C6246(S3xC2xC6):1S3432,745
(S3×C2×C6)⋊2S3 = S3×C3⋊S4φ: S3/C1 → S3 ⊆ Out S3×C2×C62412+(S3xC2xC6):2S3432,747
(S3×C2×C6)⋊3S3 = C6×D6⋊S3φ: S3/C3 → C2 ⊆ Out S3×C2×C648(S3xC2xC6):3S3432,655
(S3×C2×C6)⋊4S3 = C6×C3⋊D12φ: S3/C3 → C2 ⊆ Out S3×C2×C648(S3xC2xC6):4S3432,656
(S3×C2×C6)⋊5S3 = C3×S3×C3⋊D4φ: S3/C3 → C2 ⊆ Out S3×C2×C6244(S3xC2xC6):5S3432,658
(S3×C2×C6)⋊6S3 = C2×C33⋊6D4φ: S3/C3 → C2 ⊆ Out S3×C2×C6144(S3xC2xC6):6S3432,680
(S3×C2×C6)⋊7S3 = C2×C33⋊7D4φ: S3/C3 → C2 ⊆ Out S3×C2×C672(S3xC2xC6):7S3432,681
(S3×C2×C6)⋊8S3 = S3×C32⋊7D4φ: S3/C3 → C2 ⊆ Out S3×C2×C672(S3xC2xC6):8S3432,684
(S3×C2×C6)⋊9S3 = C22×S3×C3⋊S3φ: S3/C3 → C2 ⊆ Out S3×C2×C672(S3xC2xC6):9S3432,768

Non-split extensions G=N.Q with N=S3×C2×C6 and Q=S3
extensionφ:Q→Out NdρLabelID
(S3×C2×C6).S3 = S3×C3.S4φ: S3/C1 → S3 ⊆ Out S3×C2×C63612+(S3xC2xC6).S3432,522
(S3×C2×C6).2S3 = D6⋊Dic9φ: S3/C3 → C2 ⊆ Out S3×C2×C6144(S3xC2xC6).2S3432,93
(S3×C2×C6).3S3 = C2×S3×Dic9φ: S3/C3 → C2 ⊆ Out S3×C2×C6144(S3xC2xC6).3S3432,308
(S3×C2×C6).4S3 = C2×D6⋊D9φ: S3/C3 → C2 ⊆ Out S3×C2×C6144(S3xC2xC6).4S3432,311
(S3×C2×C6).5S3 = C2×C9⋊D12φ: S3/C3 → C2 ⊆ Out S3×C2×C672(S3xC2xC6).5S3432,312
(S3×C2×C6).6S3 = S3×C9⋊D4φ: S3/C3 → C2 ⊆ Out S3×C2×C6724(S3xC2xC6).6S3432,313
(S3×C2×C6).7S3 = C3×D6⋊Dic3φ: S3/C3 → C2 ⊆ Out S3×C2×C648(S3xC2xC6).7S3432,426
(S3×C2×C6).8S3 = C62.77D6φ: S3/C3 → C2 ⊆ Out S3×C2×C6144(S3xC2xC6).8S3432,449
(S3×C2×C6).9S3 = C22×S3×D9φ: S3/C3 → C2 ⊆ Out S3×C2×C672(S3xC2xC6).9S3432,544
(S3×C2×C6).10S3 = C2×S3×C3⋊Dic3φ: S3/C3 → C2 ⊆ Out S3×C2×C6144(S3xC2xC6).10S3432,674
(S3×C2×C6).11S3 = S3×C6×Dic3φ: trivial image48(S3xC2xC6).11S3432,651

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