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Extensions 1→N→G→Q→1 with N=C4×C12 and Q=S3

Direct product G=N×Q with N=C4×C12 and Q=S3
dρLabelID
S3×C4×C1296S3xC4xC12288,642

Semidirect products G=N:Q with N=C4×C12 and Q=S3
extensionφ:Q→Aut NdρLabelID
(C4×C12)⋊1S3 = (C4×C12)⋊S3φ: S3/C1 → S3 ⊆ Aut C4×C12366+(C4xC12):1S3288,401
(C4×C12)⋊2S3 = C3×C42⋊S3φ: S3/C1 → S3 ⊆ Aut C4×C12363(C4xC12):2S3288,397
(C4×C12)⋊3S3 = C3×C42⋊2S3φ: S3/C3 → C2 ⊆ Aut C4×C1296(C4xC12):3S3288,643
(C4×C12)⋊4S3 = C3×C42⋊3S3φ: S3/C3 → C2 ⊆ Aut C4×C1296(C4xC12):4S3288,647
(C4×C12)⋊5S3 = C122⋊2C2φ: S3/C3 → C2 ⊆ Aut C4×C12144(C4xC12):5S3288,733
(C4×C12)⋊6S3 = C12⋊4D12φ: S3/C3 → C2 ⊆ Aut C4×C12144(C4xC12):6S3288,731
(C4×C12)⋊7S3 = C122⋊6C2φ: S3/C3 → C2 ⊆ Aut C4×C12144(C4xC12):7S3288,732
(C4×C12)⋊8S3 = C122⋊C2φ: S3/C3 → C2 ⊆ Aut C4×C1272(C4xC12):8S3288,280
(C4×C12)⋊9S3 = C4×C12⋊S3φ: S3/C3 → C2 ⊆ Aut C4×C12144(C4xC12):9S3288,730
(C4×C12)⋊10S3 = C42×C3⋊S3φ: S3/C3 → C2 ⊆ Aut C4×C12144(C4xC12):10S3288,728
(C4×C12)⋊11S3 = C122⋊16C2φ: S3/C3 → C2 ⊆ Aut C4×C12144(C4xC12):11S3288,729
(C4×C12)⋊12S3 = C3×C42⋊4S3φ: S3/C3 → C2 ⊆ Aut C4×C12242(C4xC12):12S3288,239
(C4×C12)⋊13S3 = C12×D12φ: S3/C3 → C2 ⊆ Aut C4×C1296(C4xC12):13S3288,644
(C4×C12)⋊14S3 = C3×C4⋊D12φ: S3/C3 → C2 ⊆ Aut C4×C1296(C4xC12):14S3288,645
(C4×C12)⋊15S3 = C3×C42⋊7S3φ: S3/C3 → C2 ⊆ Aut C4×C1296(C4xC12):15S3288,646

Non-split extensions G=N.Q with N=C4×C12 and Q=S3
extensionφ:Q→Aut NdρLabelID
(C4×C12).S3 = C42⋊D9φ: S3/C1 → S3 ⊆ Aut C4×C12366+(C4xC12).S3288,67
(C4×C12).2S3 = C42⋊3D9φ: S3/C3 → C2 ⊆ Aut C4×C12144(C4xC12).2S3288,86
(C4×C12).3S3 = C3×C42.S3φ: S3/C3 → C2 ⊆ Aut C4×C1296(C4xC12).3S3288,237
(C4×C12).4S3 = C36⋊2Q8φ: S3/C3 → C2 ⊆ Aut C4×C12288(C4xC12).4S3288,79
(C4×C12).5S3 = C36.6Q8φ: S3/C3 → C2 ⊆ Aut C4×C12288(C4xC12).5S3288,80
(C4×C12).6S3 = C42⋊6D9φ: S3/C3 → C2 ⊆ Aut C4×C12144(C4xC12).6S3288,84
(C4×C12).7S3 = C42⋊7D9φ: S3/C3 → C2 ⊆ Aut C4×C12144(C4xC12).7S3288,85
(C4×C12).8S3 = C12⋊6Dic6φ: S3/C3 → C2 ⊆ Aut C4×C12288(C4xC12).8S3288,726
(C4×C12).9S3 = C12.25Dic6φ: S3/C3 → C2 ⊆ Aut C4×C12288(C4xC12).9S3288,727
(C4×C12).10S3 = C36⋊C8φ: S3/C3 → C2 ⊆ Aut C4×C12288(C4xC12).10S3288,11
(C4×C12).11S3 = C42⋊4D9φ: S3/C3 → C2 ⊆ Aut C4×C12722(C4xC12).11S3288,12
(C4×C12).12S3 = C4×Dic18φ: S3/C3 → C2 ⊆ Aut C4×C12288(C4xC12).12S3288,78
(C4×C12).13S3 = C4×D36φ: S3/C3 → C2 ⊆ Aut C4×C12144(C4xC12).13S3288,83
(C4×C12).14S3 = C12.57D12φ: S3/C3 → C2 ⊆ Aut C4×C12288(C4xC12).14S3288,279
(C4×C12).15S3 = C4×C32⋊4Q8φ: S3/C3 → C2 ⊆ Aut C4×C12288(C4xC12).15S3288,725
(C4×C12).16S3 = C4×C9⋊C8φ: S3/C3 → C2 ⊆ Aut C4×C12288(C4xC12).16S3288,9
(C4×C12).17S3 = C42.D9φ: S3/C3 → C2 ⊆ Aut C4×C12288(C4xC12).17S3288,10
(C4×C12).18S3 = C42×D9φ: S3/C3 → C2 ⊆ Aut C4×C12144(C4xC12).18S3288,81
(C4×C12).19S3 = C42⋊2D9φ: S3/C3 → C2 ⊆ Aut C4×C12144(C4xC12).19S3288,82
(C4×C12).20S3 = C4×C32⋊4C8φ: S3/C3 → C2 ⊆ Aut C4×C12288(C4xC12).20S3288,277
(C4×C12).21S3 = C122.C2φ: S3/C3 → C2 ⊆ Aut C4×C12288(C4xC12).21S3288,278
(C4×C12).22S3 = C3×C12⋊C8φ: S3/C3 → C2 ⊆ Aut C4×C1296(C4xC12).22S3288,238
(C4×C12).23S3 = C12×Dic6φ: S3/C3 → C2 ⊆ Aut C4×C1296(C4xC12).23S3288,639
(C4×C12).24S3 = C3×C12⋊2Q8φ: S3/C3 → C2 ⊆ Aut C4×C1296(C4xC12).24S3288,640
(C4×C12).25S3 = C3×C12.6Q8φ: S3/C3 → C2 ⊆ Aut C4×C1296(C4xC12).25S3288,641
(C4×C12).26S3 = C12×C3⋊C8central extension (φ=1)96(C4xC12).26S3288,236

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