# Extensions 1→N→G→Q→1 with N=C4×C12 and Q=C6

Direct product G=N×Q with N=C4×C12 and Q=C6
dρLabelID
C2×C122288C2xC12^2288,811

Semidirect products G=N:Q with N=C4×C12 and Q=C6
extensionφ:Q→Aut NdρLabelID
(C4×C12)⋊1C6 = C42⋊C3⋊S3φ: C6/C1C6 ⊆ Aut C4×C12486(C4xC12):1C6288,406
(C4×C12)⋊2C6 = C3×C42⋊C6φ: C6/C1C6 ⊆ Aut C4×C12486(C4xC12):2C6288,635
(C4×C12)⋊3C6 = (C4×C12)⋊C6φ: C6/C1C6 ⊆ Aut C4×C12366+(C4xC12):3C6288,405
(C4×C12)⋊4C6 = S3×C42⋊C3φ: C6/C1C6 ⊆ Aut C4×C12366(C4xC12):4C6288,407
(C4×C12)⋊5C6 = C3×C23.A4φ: C6/C1C6 ⊆ Aut C4×C12366(C4xC12):5C6288,636
(C4×C12)⋊6C6 = C6×C42⋊C3φ: C6/C2C3 ⊆ Aut C4×C12363(C4xC12):6C6288,632
(C4×C12)⋊7C6 = C3×C423S3φ: C6/C3C2 ⊆ Aut C4×C1296(C4xC12):7C6288,647
(C4×C12)⋊8C6 = C32×C42⋊C2φ: C6/C3C2 ⊆ Aut C4×C12144(C4xC12):8C6288,814
(C4×C12)⋊9C6 = C32×C422C2φ: C6/C3C2 ⊆ Aut C4×C12144(C4xC12):9C6288,823
(C4×C12)⋊10C6 = C3×C4⋊D12φ: C6/C3C2 ⊆ Aut C4×C1296(C4xC12):10C6288,645
(C4×C12)⋊11C6 = C3×C427S3φ: C6/C3C2 ⊆ Aut C4×C1296(C4xC12):11C6288,646
(C4×C12)⋊12C6 = C3×C424S3φ: C6/C3C2 ⊆ Aut C4×C12242(C4xC12):12C6288,239
(C4×C12)⋊13C6 = C12×D12φ: C6/C3C2 ⊆ Aut C4×C1296(C4xC12):13C6288,644
(C4×C12)⋊14C6 = S3×C4×C12φ: C6/C3C2 ⊆ Aut C4×C1296(C4xC12):14C6288,642
(C4×C12)⋊15C6 = C3×C422S3φ: C6/C3C2 ⊆ Aut C4×C1296(C4xC12):15C6288,643
(C4×C12)⋊16C6 = C32×C4≀C2φ: C6/C3C2 ⊆ Aut C4×C1272(C4xC12):16C6288,322
(C4×C12)⋊17C6 = D4×C3×C12φ: C6/C3C2 ⊆ Aut C4×C12144(C4xC12):17C6288,815
(C4×C12)⋊18C6 = C32×C4.4D4φ: C6/C3C2 ⊆ Aut C4×C12144(C4xC12):18C6288,821
(C4×C12)⋊19C6 = C32×C41D4φ: C6/C3C2 ⊆ Aut C4×C12144(C4xC12):19C6288,824

Non-split extensions G=N.Q with N=C4×C12 and Q=C6
extensionφ:Q→Aut NdρLabelID
(C4×C12).1C6 = C42⋊C18φ: C6/C1C6 ⊆ Aut C4×C12726(C4xC12).1C6288,74
(C4×C12).2C6 = C422C18φ: C6/C1C6 ⊆ Aut C4×C12366(C4xC12).2C6288,75
(C4×C12).3C6 = C2×C42⋊C9φ: C6/C2C3 ⊆ Aut C4×C12363(C4xC12).3C6288,71
(C4×C12).4C6 = C9×C8⋊C4φ: C6/C3C2 ⊆ Aut C4×C12288(C4xC12).4C6288,47
(C4×C12).5C6 = C9×C42⋊C2φ: C6/C3C2 ⊆ Aut C4×C12144(C4xC12).5C6288,167
(C4×C12).6C6 = C9×C422C2φ: C6/C3C2 ⊆ Aut C4×C12144(C4xC12).6C6288,176
(C4×C12).7C6 = C32×C8⋊C4φ: C6/C3C2 ⊆ Aut C4×C12288(C4xC12).7C6288,315
(C4×C12).8C6 = C3×C122Q8φ: C6/C3C2 ⊆ Aut C4×C1296(C4xC12).8C6288,640
(C4×C12).9C6 = C3×C12.6Q8φ: C6/C3C2 ⊆ Aut C4×C1296(C4xC12).9C6288,641
(C4×C12).10C6 = C3×C12⋊C8φ: C6/C3C2 ⊆ Aut C4×C1296(C4xC12).10C6288,238
(C4×C12).11C6 = C12×Dic6φ: C6/C3C2 ⊆ Aut C4×C1296(C4xC12).11C6288,639
(C4×C12).12C6 = C12×C3⋊C8φ: C6/C3C2 ⊆ Aut C4×C1296(C4xC12).12C6288,236
(C4×C12).13C6 = C3×C42.S3φ: C6/C3C2 ⊆ Aut C4×C1296(C4xC12).13C6288,237
(C4×C12).14C6 = C9×C4≀C2φ: C6/C3C2 ⊆ Aut C4×C12722(C4xC12).14C6288,54
(C4×C12).15C6 = C9×C4⋊C8φ: C6/C3C2 ⊆ Aut C4×C12288(C4xC12).15C6288,55
(C4×C12).16C6 = D4×C36φ: C6/C3C2 ⊆ Aut C4×C12144(C4xC12).16C6288,168
(C4×C12).17C6 = Q8×C36φ: C6/C3C2 ⊆ Aut C4×C12288(C4xC12).17C6288,169
(C4×C12).18C6 = C9×C4.4D4φ: C6/C3C2 ⊆ Aut C4×C12144(C4xC12).18C6288,174
(C4×C12).19C6 = C9×C42.C2φ: C6/C3C2 ⊆ Aut C4×C12288(C4xC12).19C6288,175
(C4×C12).20C6 = C9×C41D4φ: C6/C3C2 ⊆ Aut C4×C12144(C4xC12).20C6288,177
(C4×C12).21C6 = C9×C4⋊Q8φ: C6/C3C2 ⊆ Aut C4×C12288(C4xC12).21C6288,178
(C4×C12).22C6 = C32×C4⋊C8φ: C6/C3C2 ⊆ Aut C4×C12288(C4xC12).22C6288,323
(C4×C12).23C6 = Q8×C3×C12φ: C6/C3C2 ⊆ Aut C4×C12288(C4xC12).23C6288,816
(C4×C12).24C6 = C32×C42.C2φ: C6/C3C2 ⊆ Aut C4×C12288(C4xC12).24C6288,822
(C4×C12).25C6 = C32×C4⋊Q8φ: C6/C3C2 ⊆ Aut C4×C12288(C4xC12).25C6288,825

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