# Extensions 1→N→G→Q→1 with N=C2×C6×C12 and Q=C2

Direct product G=N×Q with N=C2×C6×C12 and Q=C2
dρLabelID
C22×C6×C12288C2^2xC6xC12288,1018

Semidirect products G=N:Q with N=C2×C6×C12 and Q=C2
extensionφ:Q→Aut NdρLabelID
(C2×C6×C12)⋊1C2 = C6×D6⋊C4φ: C2/C1C2 ⊆ Aut C2×C6×C1296(C2xC6xC12):1C2288,698
(C2×C6×C12)⋊2C2 = C3×C23.28D6φ: C2/C1C2 ⊆ Aut C2×C6×C1248(C2xC6xC12):2C2288,700
(C2×C6×C12)⋊3C2 = C2×C6.11D12φ: C2/C1C2 ⊆ Aut C2×C6×C12144(C2xC6xC12):3C2288,784
(C2×C6×C12)⋊4C2 = C62.129D4φ: C2/C1C2 ⊆ Aut C2×C6×C12144(C2xC6xC12):4C2288,786
(C2×C6×C12)⋊5C2 = C22⋊C4×C3×C6φ: C2/C1C2 ⊆ Aut C2×C6×C12144(C2xC6xC12):5C2288,812
(C2×C6×C12)⋊6C2 = D4×C3×C12φ: C2/C1C2 ⊆ Aut C2×C6×C12144(C2xC6xC12):6C2288,815
(C2×C6×C12)⋊7C2 = C32×C22.D4φ: C2/C1C2 ⊆ Aut C2×C6×C12144(C2xC6xC12):7C2288,820
(C2×C6×C12)⋊8C2 = C6219D4φ: C2/C1C2 ⊆ Aut C2×C6×C12144(C2xC6xC12):8C2288,787
(C2×C6×C12)⋊9C2 = C22×C12⋊S3φ: C2/C1C2 ⊆ Aut C2×C6×C12144(C2xC6xC12):9C2288,1005
(C2×C6×C12)⋊10C2 = C2×C12.59D6φ: C2/C1C2 ⊆ Aut C2×C6×C12144(C2xC6xC12):10C2288,1006
(C2×C6×C12)⋊11C2 = C6×C4○D12φ: C2/C1C2 ⊆ Aut C2×C6×C1248(C2xC6xC12):11C2288,991
(C2×C6×C12)⋊12C2 = C3×C127D4φ: C2/C1C2 ⊆ Aut C2×C6×C1248(C2xC6xC12):12C2288,701
(C2×C6×C12)⋊13C2 = C2×C6×D12φ: C2/C1C2 ⊆ Aut C2×C6×C1296(C2xC6xC12):13C2288,990
(C2×C6×C12)⋊14C2 = C12×C3⋊D4φ: C2/C1C2 ⊆ Aut C2×C6×C1248(C2xC6xC12):14C2288,699
(C2×C6×C12)⋊15C2 = C4×C327D4φ: C2/C1C2 ⊆ Aut C2×C6×C12144(C2xC6xC12):15C2288,785
(C2×C6×C12)⋊16C2 = S3×C22×C12φ: C2/C1C2 ⊆ Aut C2×C6×C1296(C2xC6xC12):16C2288,989
(C2×C6×C12)⋊17C2 = C22×C4×C3⋊S3φ: C2/C1C2 ⊆ Aut C2×C6×C12144(C2xC6xC12):17C2288,1004
(C2×C6×C12)⋊18C2 = C32×C4⋊D4φ: C2/C1C2 ⊆ Aut C2×C6×C12144(C2xC6xC12):18C2288,818
(C2×C6×C12)⋊19C2 = D4×C62φ: C2/C1C2 ⊆ Aut C2×C6×C12144(C2xC6xC12):19C2288,1019
(C2×C6×C12)⋊20C2 = C4○D4×C3×C6φ: C2/C1C2 ⊆ Aut C2×C6×C12144(C2xC6xC12):20C2288,1021

Non-split extensions G=N.Q with N=C2×C6×C12 and Q=C2
extensionφ:Q→Aut NdρLabelID
(C2×C6×C12).1C2 = C3×C6.C42φ: C2/C1C2 ⊆ Aut C2×C6×C1296(C2xC6xC12).1C2288,265
(C2×C6×C12).2C2 = C62.15Q8φ: C2/C1C2 ⊆ Aut C2×C6×C12288(C2xC6xC12).2C2288,306
(C2×C6×C12).3C2 = C32×C2.C42φ: C2/C1C2 ⊆ Aut C2×C6×C12288(C2xC6xC12).3C2288,313
(C2×C6×C12).4C2 = C32×C22⋊C8φ: C2/C1C2 ⊆ Aut C2×C6×C12144(C2xC6xC12).4C2288,316
(C2×C6×C12).5C2 = C6×Dic3⋊C4φ: C2/C1C2 ⊆ Aut C2×C6×C1296(C2xC6xC12).5C2288,694
(C2×C6×C12).6C2 = C2×C6.Dic6φ: C2/C1C2 ⊆ Aut C2×C6×C12288(C2xC6xC12).6C2288,780
(C2×C6×C12).7C2 = C4⋊C4×C3×C6φ: C2/C1C2 ⊆ Aut C2×C6×C12288(C2xC6xC12).7C2288,813
(C2×C6×C12).8C2 = C6210Q8φ: C2/C1C2 ⊆ Aut C2×C6×C12144(C2xC6xC12).8C2288,781
(C2×C6×C12).9C2 = C2×C12⋊Dic3φ: C2/C1C2 ⊆ Aut C2×C6×C12288(C2xC6xC12).9C2288,782
(C2×C6×C12).10C2 = C22×C324Q8φ: C2/C1C2 ⊆ Aut C2×C6×C12288(C2xC6xC12).10C2288,1003
(C2×C6×C12).11C2 = C2×C12.58D6φ: C2/C1C2 ⊆ Aut C2×C6×C12144(C2xC6xC12).11C2288,778
(C2×C6×C12).12C2 = C62.247C23φ: C2/C1C2 ⊆ Aut C2×C6×C12144(C2xC6xC12).12C2288,783
(C2×C6×C12).13C2 = C6×C4.Dic3φ: C2/C1C2 ⊆ Aut C2×C6×C1248(C2xC6xC12).13C2288,692
(C2×C6×C12).14C2 = C3×C23.26D6φ: C2/C1C2 ⊆ Aut C2×C6×C1248(C2xC6xC12).14C2288,697
(C2×C6×C12).15C2 = C3×C12.48D4φ: C2/C1C2 ⊆ Aut C2×C6×C1248(C2xC6xC12).15C2288,695
(C2×C6×C12).16C2 = C6×C4⋊Dic3φ: C2/C1C2 ⊆ Aut C2×C6×C1296(C2xC6xC12).16C2288,696
(C2×C6×C12).17C2 = C2×C6×Dic6φ: C2/C1C2 ⊆ Aut C2×C6×C1296(C2xC6xC12).17C2288,988
(C2×C6×C12).18C2 = C3×C12.55D4φ: C2/C1C2 ⊆ Aut C2×C6×C1248(C2xC6xC12).18C2288,264
(C2×C6×C12).19C2 = C627C8φ: C2/C1C2 ⊆ Aut C2×C6×C12144(C2xC6xC12).19C2288,305
(C2×C6×C12).20C2 = C2×C6×C3⋊C8φ: C2/C1C2 ⊆ Aut C2×C6×C1296(C2xC6xC12).20C2288,691
(C2×C6×C12).21C2 = Dic3×C2×C12φ: C2/C1C2 ⊆ Aut C2×C6×C1296(C2xC6xC12).21C2288,693
(C2×C6×C12).22C2 = C22×C324C8φ: C2/C1C2 ⊆ Aut C2×C6×C12288(C2xC6xC12).22C2288,777
(C2×C6×C12).23C2 = C2×C4×C3⋊Dic3φ: C2/C1C2 ⊆ Aut C2×C6×C12288(C2xC6xC12).23C2288,779
(C2×C6×C12).24C2 = C32×C42⋊C2φ: C2/C1C2 ⊆ Aut C2×C6×C12144(C2xC6xC12).24C2288,814
(C2×C6×C12).25C2 = C32×C22⋊Q8φ: C2/C1C2 ⊆ Aut C2×C6×C12144(C2xC6xC12).25C2288,819
(C2×C6×C12).26C2 = M4(2)×C3×C6φ: C2/C1C2 ⊆ Aut C2×C6×C12144(C2xC6xC12).26C2288,827
(C2×C6×C12).27C2 = Q8×C62φ: C2/C1C2 ⊆ Aut C2×C6×C12288(C2xC6xC12).27C2288,1020

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