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

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

Semidirect products G=N:Q with N=C6×C12 and Q=C4
extensionφ:Q→Aut NdρLabelID
(C6×C12)⋊1C4 = (C6×C12)⋊C4φ: C4/C1 → C4 ⊆ Aut C6×C12244+(C6xC12):1C4288,422
(C6×C12)⋊2C4 = (C6×C12)⋊2C4φ: C4/C1 → C4 ⊆ Aut C6×C1248(C6xC12):2C4288,429
(C6×C12)⋊3C4 = C2×C4×C32⋊C4φ: C4/C1 → C4 ⊆ Aut C6×C1248(C6xC12):3C4288,932
(C6×C12)⋊4C4 = C2×C4⋊(C32⋊C4)φ: C4/C1 → C4 ⊆ Aut C6×C1248(C6xC12):4C4288,933
(C6×C12)⋊5C4 = (C6×C12)⋊5C4φ: C4/C1 → C4 ⊆ Aut C6×C12244(C6xC12):5C4288,934
(C6×C12)⋊6C4 = C3×C23.7D6φ: C4/C1 → C4 ⊆ Aut C6×C12244(C6xC12):6C4288,268
(C6×C12)⋊7C4 = C62.38D4φ: C4/C1 → C4 ⊆ Aut C6×C1272(C6xC12):7C4288,309
(C6×C12)⋊8C4 = C32×C23⋊C4φ: C4/C1 → C4 ⊆ Aut C6×C1272(C6xC12):8C4288,317
(C6×C12)⋊9C4 = C3×C6.C42φ: C4/C2 → C2 ⊆ Aut C6×C1296(C6xC12):9C4288,265
(C6×C12)⋊10C4 = C62.15Q8φ: C4/C2 → C2 ⊆ Aut C6×C12288(C6xC12):10C4288,306
(C6×C12)⋊11C4 = C32×C2.C42φ: C4/C2 → C2 ⊆ Aut C6×C12288(C6xC12):11C4288,313
(C6×C12)⋊12C4 = C2×C12⋊Dic3φ: C4/C2 → C2 ⊆ Aut C6×C12288(C6xC12):12C4288,782
(C6×C12)⋊13C4 = C62.247C23φ: C4/C2 → C2 ⊆ Aut C6×C12144(C6xC12):13C4288,783
(C6×C12)⋊14C4 = C3×C23.26D6φ: C4/C2 → C2 ⊆ Aut C6×C1248(C6xC12):14C4288,697
(C6×C12)⋊15C4 = C6×C4⋊Dic3φ: C4/C2 → C2 ⊆ Aut C6×C1296(C6xC12):15C4288,696
(C6×C12)⋊16C4 = Dic3×C2×C12φ: C4/C2 → C2 ⊆ Aut C6×C1296(C6xC12):16C4288,693
(C6×C12)⋊17C4 = C2×C4×C3⋊Dic3φ: C4/C2 → C2 ⊆ Aut C6×C12288(C6xC12):17C4288,779
(C6×C12)⋊18C4 = C4⋊C4×C3×C6φ: C4/C2 → C2 ⊆ Aut C6×C12288(C6xC12):18C4288,813
(C6×C12)⋊19C4 = C32×C42⋊C2φ: C4/C2 → C2 ⊆ Aut C6×C12144(C6xC12):19C4288,814

Non-split extensions G=N.Q with N=C6×C12 and Q=C4
extensionφ:Q→Aut NdρLabelID
(C6×C12).1C4 = C3⋊Dic3.D4φ: C4/C1 → C4 ⊆ Aut C6×C12484-(C6xC12).1C4288,428
(C6×C12).2C4 = C2×C32⋊2C16φ: C4/C1 → C4 ⊆ Aut C6×C1296(C6xC12).2C4288,420
(C6×C12).3C4 = C62.4C8φ: C4/C1 → C4 ⊆ Aut C6×C12484(C6xC12).3C4288,421
(C6×C12).4C4 = C4×C32⋊2C8φ: C4/C1 → C4 ⊆ Aut C6×C1296(C6xC12).4C4288,423
(C6×C12).5C4 = (C3×C12)⋊4C8φ: C4/C1 → C4 ⊆ Aut C6×C1296(C6xC12).5C4288,424
(C6×C12).6C4 = C32⋊2C8⋊C4φ: C4/C1 → C4 ⊆ Aut C6×C1296(C6xC12).6C4288,425
(C6×C12).7C4 = C62.6(C2×C4)φ: C4/C1 → C4 ⊆ Aut C6×C1248(C6xC12).7C4288,426
(C6×C12).8C4 = C32⋊5(C4⋊C8)φ: C4/C1 → C4 ⊆ Aut C6×C1296(C6xC12).8C4288,427
(C6×C12).9C4 = C2×C3⋊S3⋊3C8φ: C4/C1 → C4 ⊆ Aut C6×C1248(C6xC12).9C4288,929
(C6×C12).10C4 = C2×C32⋊M4(2)φ: C4/C1 → C4 ⊆ Aut C6×C1248(C6xC12).10C4288,930
(C6×C12).11C4 = C3⋊S3⋊M4(2)φ: C4/C1 → C4 ⊆ Aut C6×C12244(C6xC12).11C4288,931
(C6×C12).12C4 = C3×C12.10D4φ: C4/C1 → C4 ⊆ Aut C6×C12484(C6xC12).12C4288,270
(C6×C12).13C4 = (C6×C12).C4φ: C4/C1 → C4 ⊆ Aut C6×C12144(C6xC12).13C4288,311
(C6×C12).14C4 = C32×C4.10D4φ: C4/C1 → C4 ⊆ Aut C6×C12144(C6xC12).14C4288,319
(C6×C12).15C4 = C3×C42.S3φ: C4/C2 → C2 ⊆ Aut C6×C1296(C6xC12).15C4288,237
(C6×C12).16C4 = C3×C12⋊C8φ: C4/C2 → C2 ⊆ Aut C6×C1296(C6xC12).16C4288,238
(C6×C12).17C4 = C3×C12.55D4φ: C4/C2 → C2 ⊆ Aut C6×C1248(C6xC12).17C4288,264
(C6×C12).18C4 = C122.C2φ: C4/C2 → C2 ⊆ Aut C6×C12288(C6xC12).18C4288,278
(C6×C12).19C4 = C12.57D12φ: C4/C2 → C2 ⊆ Aut C6×C12288(C6xC12).19C4288,279
(C6×C12).20C4 = C62⋊7C8φ: C4/C2 → C2 ⊆ Aut C6×C12144(C6xC12).20C4288,305
(C6×C12).21C4 = C32×C8⋊C4φ: C4/C2 → C2 ⊆ Aut C6×C12288(C6xC12).21C4288,315
(C6×C12).22C4 = C32×C22⋊C8φ: C4/C2 → C2 ⊆ Aut C6×C12144(C6xC12).22C4288,316
(C6×C12).23C4 = C32×C4⋊C8φ: C4/C2 → C2 ⊆ Aut C6×C12288(C6xC12).23C4288,323
(C6×C12).24C4 = C24.94D6φ: C4/C2 → C2 ⊆ Aut C6×C12144(C6xC12).24C4288,287
(C6×C12).25C4 = C2×C12.58D6φ: C4/C2 → C2 ⊆ Aut C6×C12144(C6xC12).25C4288,778
(C6×C12).26C4 = C3×C12.C8φ: C4/C2 → C2 ⊆ Aut C6×C12482(C6xC12).26C4288,246
(C6×C12).27C4 = C6×C4.Dic3φ: C4/C2 → C2 ⊆ Aut C6×C1248(C6xC12).27C4288,692
(C6×C12).28C4 = C12×C3⋊C8φ: C4/C2 → C2 ⊆ Aut C6×C1296(C6xC12).28C4288,236
(C6×C12).29C4 = C6×C3⋊C16φ: C4/C2 → C2 ⊆ Aut C6×C1296(C6xC12).29C4288,245
(C6×C12).30C4 = C4×C32⋊4C8φ: C4/C2 → C2 ⊆ Aut C6×C12288(C6xC12).30C4288,277
(C6×C12).31C4 = C2×C24.S3φ: C4/C2 → C2 ⊆ Aut C6×C12288(C6xC12).31C4288,286
(C6×C12).32C4 = C2×C6×C3⋊C8φ: C4/C2 → C2 ⊆ Aut C6×C1296(C6xC12).32C4288,691
(C6×C12).33C4 = C22×C32⋊4C8φ: C4/C2 → C2 ⊆ Aut C6×C12288(C6xC12).33C4288,777
(C6×C12).34C4 = C32×M5(2)φ: C4/C2 → C2 ⊆ Aut C6×C12144(C6xC12).34C4288,328
(C6×C12).35C4 = M4(2)×C3×C6φ: C4/C2 → C2 ⊆ Aut C6×C12144(C6xC12).35C4288,827

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