# Extensions 1→N→G→Q→1 with N=C3×C6×C12 and Q=C2

Direct product G=N×Q with N=C3×C6×C12 and Q=C2
dρLabelID
C62×C12432C6^2xC12432,730

Semidirect products G=N:Q with N=C3×C6×C12 and Q=C2
extensionφ:Q→Aut NdρLabelID
(C3×C6×C12)⋊1C2 = C32×D6⋊C4φ: C2/C1C2 ⊆ Aut C3×C6×C12144(C3xC6xC12):1C2432,474
(C3×C6×C12)⋊2C2 = C3×C6.11D12φ: C2/C1C2 ⊆ Aut C3×C6×C12144(C3xC6xC12):2C2432,490
(C3×C6×C12)⋊3C2 = C62.148D6φ: C2/C1C2 ⊆ Aut C3×C6×C12216(C3xC6xC12):3C2432,506
(C3×C6×C12)⋊4C2 = C22⋊C4×C33φ: C2/C1C2 ⊆ Aut C3×C6×C12216(C3xC6xC12):4C2432,513
(C3×C6×C12)⋊5C2 = C2×C3312D4φ: C2/C1C2 ⊆ Aut C3×C6×C12216(C3xC6xC12):5C2432,722
(C3×C6×C12)⋊6C2 = C62.160D6φ: C2/C1C2 ⊆ Aut C3×C6×C12216(C3xC6xC12):6C2432,723
(C3×C6×C12)⋊7C2 = C32×C4○D12φ: C2/C1C2 ⊆ Aut C3×C6×C1272(C3xC6xC12):7C2432,703
(C3×C6×C12)⋊8C2 = C3×C12.59D6φ: C2/C1C2 ⊆ Aut C3×C6×C1272(C3xC6xC12):8C2432,713
(C3×C6×C12)⋊9C2 = C3×C6×D12φ: C2/C1C2 ⊆ Aut C3×C6×C12144(C3xC6xC12):9C2432,702
(C3×C6×C12)⋊10C2 = C6×C12⋊S3φ: C2/C1C2 ⊆ Aut C3×C6×C12144(C3xC6xC12):10C2432,712
(C3×C6×C12)⋊11C2 = S3×C6×C12φ: C2/C1C2 ⊆ Aut C3×C6×C12144(C3xC6xC12):11C2432,701
(C3×C6×C12)⋊12C2 = C3⋊S3×C2×C12φ: C2/C1C2 ⊆ Aut C3×C6×C12144(C3xC6xC12):12C2432,711
(C3×C6×C12)⋊13C2 = C2×C4×C33⋊C2φ: C2/C1C2 ⊆ Aut C3×C6×C12216(C3xC6xC12):13C2432,721
(C3×C6×C12)⋊14C2 = D4×C32×C6φ: C2/C1C2 ⊆ Aut C3×C6×C12216(C3xC6xC12):14C2432,731
(C3×C6×C12)⋊15C2 = C4○D4×C33φ: C2/C1C2 ⊆ Aut C3×C6×C12216(C3xC6xC12):15C2432,733

Non-split extensions G=N.Q with N=C3×C6×C12 and Q=C2
extensionφ:Q→Aut NdρLabelID
(C3×C6×C12).1C2 = C32×Dic3⋊C4φ: C2/C1C2 ⊆ Aut C3×C6×C12144(C3xC6xC12).1C2432,472
(C3×C6×C12).2C2 = C3×C6.Dic6φ: C2/C1C2 ⊆ Aut C3×C6×C12144(C3xC6xC12).2C2432,488
(C3×C6×C12).3C2 = C62.146D6φ: C2/C1C2 ⊆ Aut C3×C6×C12432(C3xC6xC12).3C2432,504
(C3×C6×C12).4C2 = C62.147D6φ: C2/C1C2 ⊆ Aut C3×C6×C12432(C3xC6xC12).4C2432,505
(C3×C6×C12).5C2 = C2×C338Q8φ: C2/C1C2 ⊆ Aut C3×C6×C12432(C3xC6xC12).5C2432,720
(C3×C6×C12).6C2 = C3318M4(2)φ: C2/C1C2 ⊆ Aut C3×C6×C12216(C3xC6xC12).6C2432,502
(C3×C6×C12).7C2 = C32×C4.Dic3φ: C2/C1C2 ⊆ Aut C3×C6×C1272(C3xC6xC12).7C2432,470
(C3×C6×C12).8C2 = C3×C12.58D6φ: C2/C1C2 ⊆ Aut C3×C6×C1272(C3xC6xC12).8C2432,486
(C3×C6×C12).9C2 = C32×C4⋊Dic3φ: C2/C1C2 ⊆ Aut C3×C6×C12144(C3xC6xC12).9C2432,473
(C3×C6×C12).10C2 = C3×C12⋊Dic3φ: C2/C1C2 ⊆ Aut C3×C6×C12144(C3xC6xC12).10C2432,489
(C3×C6×C12).11C2 = C3×C6×Dic6φ: C2/C1C2 ⊆ Aut C3×C6×C12144(C3xC6xC12).11C2432,700
(C3×C6×C12).12C2 = C6×C324Q8φ: C2/C1C2 ⊆ Aut C3×C6×C12144(C3xC6xC12).12C2432,710
(C3×C6×C12).13C2 = C3×C6×C3⋊C8φ: C2/C1C2 ⊆ Aut C3×C6×C12144(C3xC6xC12).13C2432,469
(C3×C6×C12).14C2 = Dic3×C3×C12φ: C2/C1C2 ⊆ Aut C3×C6×C12144(C3xC6xC12).14C2432,471
(C3×C6×C12).15C2 = C6×C324C8φ: C2/C1C2 ⊆ Aut C3×C6×C12144(C3xC6xC12).15C2432,485
(C3×C6×C12).16C2 = C12×C3⋊Dic3φ: C2/C1C2 ⊆ Aut C3×C6×C12144(C3xC6xC12).16C2432,487
(C3×C6×C12).17C2 = C2×C337C8φ: C2/C1C2 ⊆ Aut C3×C6×C12432(C3xC6xC12).17C2432,501
(C3×C6×C12).18C2 = C4×C335C4φ: C2/C1C2 ⊆ Aut C3×C6×C12432(C3xC6xC12).18C2432,503
(C3×C6×C12).19C2 = C4⋊C4×C33φ: C2/C1C2 ⊆ Aut C3×C6×C12432(C3xC6xC12).19C2432,514
(C3×C6×C12).20C2 = M4(2)×C33φ: C2/C1C2 ⊆ Aut C3×C6×C12216(C3xC6xC12).20C2432,516
(C3×C6×C12).21C2 = Q8×C32×C6φ: C2/C1C2 ⊆ Aut C3×C6×C12432(C3xC6xC12).21C2432,732

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