# Extensions 1→N→G→Q→1 with N=C2×C12 and Q=S3

Direct product G=N×Q with N=C2×C12 and Q=S3
dρLabelID
S3×C2×C1248S3xC2xC12144,159

Semidirect products G=N:Q with N=C2×C12 and Q=S3
extensionφ:Q→Aut NdρLabelID
(C2×C12)⋊1S3 = C3×D6⋊C4φ: S3/C3C2 ⊆ Aut C2×C1248(C2xC12):1S3144,79
(C2×C12)⋊2S3 = C6.11D12φ: S3/C3C2 ⊆ Aut C2×C1272(C2xC12):2S3144,95
(C2×C12)⋊3S3 = C2×C12⋊S3φ: S3/C3C2 ⊆ Aut C2×C1272(C2xC12):3S3144,170
(C2×C12)⋊4S3 = C12.59D6φ: S3/C3C2 ⊆ Aut C2×C1272(C2xC12):4S3144,171
(C2×C12)⋊5S3 = C2×C4×C3⋊S3φ: S3/C3C2 ⊆ Aut C2×C1272(C2xC12):5S3144,169
(C2×C12)⋊6S3 = C6×D12φ: S3/C3C2 ⊆ Aut C2×C1248(C2xC12):6S3144,160
(C2×C12)⋊7S3 = C3×C4○D12φ: S3/C3C2 ⊆ Aut C2×C12242(C2xC12):7S3144,161

Non-split extensions G=N.Q with N=C2×C12 and Q=S3
extensionφ:Q→Aut NdρLabelID
(C2×C12).1S3 = Dic9⋊C4φ: S3/C3C2 ⊆ Aut C2×C12144(C2xC12).1S3144,12
(C2×C12).2S3 = D18⋊C4φ: S3/C3C2 ⊆ Aut C2×C1272(C2xC12).2S3144,14
(C2×C12).3S3 = C3×Dic3⋊C4φ: S3/C3C2 ⊆ Aut C2×C1248(C2xC12).3S3144,77
(C2×C12).4S3 = C6.Dic6φ: S3/C3C2 ⊆ Aut C2×C12144(C2xC12).4S3144,93
(C2×C12).5S3 = C4⋊Dic9φ: S3/C3C2 ⊆ Aut C2×C12144(C2xC12).5S3144,13
(C2×C12).6S3 = C2×Dic18φ: S3/C3C2 ⊆ Aut C2×C12144(C2xC12).6S3144,37
(C2×C12).7S3 = C2×D36φ: S3/C3C2 ⊆ Aut C2×C1272(C2xC12).7S3144,39
(C2×C12).8S3 = C12⋊Dic3φ: S3/C3C2 ⊆ Aut C2×C12144(C2xC12).8S3144,94
(C2×C12).9S3 = C2×C324Q8φ: S3/C3C2 ⊆ Aut C2×C12144(C2xC12).9S3144,168
(C2×C12).10S3 = C4.Dic9φ: S3/C3C2 ⊆ Aut C2×C12722(C2xC12).10S3144,10
(C2×C12).11S3 = D365C2φ: S3/C3C2 ⊆ Aut C2×C12722(C2xC12).11S3144,40
(C2×C12).12S3 = C12.58D6φ: S3/C3C2 ⊆ Aut C2×C1272(C2xC12).12S3144,91
(C2×C12).13S3 = C2×C9⋊C8φ: S3/C3C2 ⊆ Aut C2×C12144(C2xC12).13S3144,9
(C2×C12).14S3 = C4×Dic9φ: S3/C3C2 ⊆ Aut C2×C12144(C2xC12).14S3144,11
(C2×C12).15S3 = C2×C4×D9φ: S3/C3C2 ⊆ Aut C2×C1272(C2xC12).15S3144,38
(C2×C12).16S3 = C2×C324C8φ: S3/C3C2 ⊆ Aut C2×C12144(C2xC12).16S3144,90
(C2×C12).17S3 = C4×C3⋊Dic3φ: S3/C3C2 ⊆ Aut C2×C12144(C2xC12).17S3144,92
(C2×C12).18S3 = C3×C4.Dic3φ: S3/C3C2 ⊆ Aut C2×C12242(C2xC12).18S3144,75
(C2×C12).19S3 = C3×C4⋊Dic3φ: S3/C3C2 ⊆ Aut C2×C1248(C2xC12).19S3144,78
(C2×C12).20S3 = C6×Dic6φ: S3/C3C2 ⊆ Aut C2×C1248(C2xC12).20S3144,158
(C2×C12).21S3 = C6×C3⋊C8central extension (φ=1)48(C2xC12).21S3144,74
(C2×C12).22S3 = Dic3×C12central extension (φ=1)48(C2xC12).22S3144,76

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