# Extensions 1→N→G→Q→1 with N=C2×C4×C12 and Q=C2

Direct product G=N×Q with N=C2×C4×C12 and Q=C2
dρLabelID
C22×C4×C12192C2^2xC4xC12192,1400

Semidirect products G=N:Q with N=C2×C4×C12 and Q=C2
extensionφ:Q→Aut NdρLabelID
(C2×C4×C12)⋊1C2 = (C2×C42)⋊3S3φ: C2/C1C2 ⊆ Aut C2×C4×C1296(C2xC4xC12):1C2192,499
(C2×C4×C12)⋊2C2 = C12×C22⋊C4φ: C2/C1C2 ⊆ Aut C2×C4×C1296(C2xC4xC12):2C2192,810
(C2×C4×C12)⋊3C2 = C3×C24.C22φ: C2/C1C2 ⊆ Aut C2×C4×C1296(C2xC4xC12):3C2192,821
(C2×C4×C12)⋊4C2 = C2×C423S3φ: C2/C1C2 ⊆ Aut C2×C4×C1296(C2xC4xC12):4C2192,1037
(C2×C4×C12)⋊5C2 = C6×C42⋊C2φ: C2/C1C2 ⊆ Aut C2×C4×C1296(C2xC4xC12):5C2192,1403
(C2×C4×C12)⋊6C2 = C6×C422C2φ: C2/C1C2 ⊆ Aut C2×C4×C1296(C2xC4xC12):6C2192,1417
(C2×C4×C12)⋊7C2 = (C2×C4)⋊6D12φ: C2/C1C2 ⊆ Aut C2×C4×C1296(C2xC4xC12):7C2192,498
(C2×C4×C12)⋊8C2 = C2×C4⋊D12φ: C2/C1C2 ⊆ Aut C2×C4×C1296(C2xC4xC12):8C2192,1034
(C2×C4×C12)⋊9C2 = C2×C427S3φ: C2/C1C2 ⊆ Aut C2×C4×C1296(C2xC4xC12):9C2192,1035
(C2×C4×C12)⋊10C2 = C2×C424S3φ: C2/C1C2 ⊆ Aut C2×C4×C1248(C2xC4xC12):10C2192,486
(C2×C4×C12)⋊11C2 = C2×C4×D12φ: C2/C1C2 ⊆ Aut C2×C4×C1296(C2xC4xC12):11C2192,1032
(C2×C4×C12)⋊12C2 = C4×C4○D12φ: C2/C1C2 ⊆ Aut C2×C4×C1296(C2xC4xC12):12C2192,1033
(C2×C4×C12)⋊13C2 = C42.276D6φ: C2/C1C2 ⊆ Aut C2×C4×C1296(C2xC4xC12):13C2192,1036
(C2×C4×C12)⋊14C2 = C42.277D6φ: C2/C1C2 ⊆ Aut C2×C4×C1296(C2xC4xC12):14C2192,1038
(C2×C4×C12)⋊15C2 = C4×D6⋊C4φ: C2/C1C2 ⊆ Aut C2×C4×C1296(C2xC4xC12):15C2192,497
(C2×C4×C12)⋊16C2 = S3×C2×C42φ: C2/C1C2 ⊆ Aut C2×C4×C1296(C2xC4xC12):16C2192,1030
(C2×C4×C12)⋊17C2 = C2×C422S3φ: C2/C1C2 ⊆ Aut C2×C4×C1296(C2xC4xC12):17C2192,1031
(C2×C4×C12)⋊18C2 = C3×C24.3C22φ: C2/C1C2 ⊆ Aut C2×C4×C1296(C2xC4xC12):18C2192,823
(C2×C4×C12)⋊19C2 = C6×C4≀C2φ: C2/C1C2 ⊆ Aut C2×C4×C1248(C2xC4xC12):19C2192,853
(C2×C4×C12)⋊20C2 = D4×C2×C12φ: C2/C1C2 ⊆ Aut C2×C4×C1296(C2xC4xC12):20C2192,1404
(C2×C4×C12)⋊21C2 = C12×C4○D4φ: C2/C1C2 ⊆ Aut C2×C4×C1296(C2xC4xC12):21C2192,1406
(C2×C4×C12)⋊22C2 = C6×C4.4D4φ: C2/C1C2 ⊆ Aut C2×C4×C1296(C2xC4xC12):22C2192,1415
(C2×C4×C12)⋊23C2 = C3×C23.36C23φ: C2/C1C2 ⊆ Aut C2×C4×C1296(C2xC4xC12):23C2192,1418
(C2×C4×C12)⋊24C2 = C6×C41D4φ: C2/C1C2 ⊆ Aut C2×C4×C1296(C2xC4xC12):24C2192,1419
(C2×C4×C12)⋊25C2 = C3×C22.26C24φ: C2/C1C2 ⊆ Aut C2×C4×C1296(C2xC4xC12):25C2192,1421

Non-split extensions G=N.Q with N=C2×C4×C12 and Q=C2
extensionφ:Q→Aut NdρLabelID
(C2×C4×C12).1C2 = C3×C22.7C42φ: C2/C1C2 ⊆ Aut C2×C4×C12192(C2xC4xC12).1C2192,142
(C2×C4×C12).2C2 = (C2×C42).6S3φ: C2/C1C2 ⊆ Aut C2×C4×C12192(C2xC4xC12).2C2192,492
(C2×C4×C12).3C2 = C427Dic3φ: C2/C1C2 ⊆ Aut C2×C4×C12192(C2xC4xC12).3C2192,496
(C2×C4×C12).4C2 = C3×C424C4φ: C2/C1C2 ⊆ Aut C2×C4×C12192(C2xC4xC12).4C2192,809
(C2×C4×C12).5C2 = C12×C4⋊C4φ: C2/C1C2 ⊆ Aut C2×C4×C12192(C2xC4xC12).5C2192,811
(C2×C4×C12).6C2 = C3×C425C4φ: C2/C1C2 ⊆ Aut C2×C4×C12192(C2xC4xC12).6C2192,816
(C2×C4×C12).7C2 = C3×C23.63C23φ: C2/C1C2 ⊆ Aut C2×C4×C12192(C2xC4xC12).7C2192,820
(C2×C4×C12).8C2 = C6×C8⋊C4φ: C2/C1C2 ⊆ Aut C2×C4×C12192(C2xC4xC12).8C2192,836
(C2×C4×C12).9C2 = C124(C4⋊C4)φ: C2/C1C2 ⊆ Aut C2×C4×C12192(C2xC4xC12).9C2192,487
(C2×C4×C12).10C2 = (C2×Dic6)⋊7C4φ: C2/C1C2 ⊆ Aut C2×C4×C12192(C2xC4xC12).10C2192,488
(C2×C4×C12).11C2 = C4210Dic3φ: C2/C1C2 ⊆ Aut C2×C4×C12192(C2xC4xC12).11C2192,494
(C2×C4×C12).12C2 = C4211Dic3φ: C2/C1C2 ⊆ Aut C2×C4×C12192(C2xC4xC12).12C2192,495
(C2×C4×C12).13C2 = C2×C122Q8φ: C2/C1C2 ⊆ Aut C2×C4×C12192(C2xC4xC12).13C2192,1027
(C2×C4×C12).14C2 = C2×C12.6Q8φ: C2/C1C2 ⊆ Aut C2×C4×C12192(C2xC4xC12).14C2192,1028
(C2×C4×C12).15C2 = C12.8C42φ: C2/C1C2 ⊆ Aut C2×C4×C1248(C2xC4xC12).15C2192,82
(C2×C4×C12).16C2 = C4×C4.Dic3φ: C2/C1C2 ⊆ Aut C2×C4×C1296(C2xC4xC12).16C2192,481
(C2×C4×C12).17C2 = C2×C12⋊C8φ: C2/C1C2 ⊆ Aut C2×C4×C12192(C2xC4xC12).17C2192,482
(C2×C4×C12).18C2 = C127M4(2)φ: C2/C1C2 ⊆ Aut C2×C4×C1296(C2xC4xC12).18C2192,483
(C2×C4×C12).19C2 = C42.285D6φ: C2/C1C2 ⊆ Aut C2×C4×C1296(C2xC4xC12).19C2192,484
(C2×C4×C12).20C2 = C42.270D6φ: C2/C1C2 ⊆ Aut C2×C4×C1296(C2xC4xC12).20C2192,485
(C2×C4×C12).21C2 = C4×C4⋊Dic3φ: C2/C1C2 ⊆ Aut C2×C4×C12192(C2xC4xC12).21C2192,493
(C2×C4×C12).22C2 = C2×C4×Dic6φ: C2/C1C2 ⊆ Aut C2×C4×C12192(C2xC4xC12).22C2192,1026
(C2×C4×C12).23C2 = C42.274D6φ: C2/C1C2 ⊆ Aut C2×C4×C1296(C2xC4xC12).23C2192,1029
(C2×C4×C12).24C2 = (C2×C12)⋊3C8φ: C2/C1C2 ⊆ Aut C2×C4×C12192(C2xC4xC12).24C2192,83
(C2×C4×C12).25C2 = C2×C4×C3⋊C8φ: C2/C1C2 ⊆ Aut C2×C4×C12192(C2xC4xC12).25C2192,479
(C2×C4×C12).26C2 = C2×C42.S3φ: C2/C1C2 ⊆ Aut C2×C4×C12192(C2xC4xC12).26C2192,480
(C2×C4×C12).27C2 = Dic3×C42φ: C2/C1C2 ⊆ Aut C2×C4×C12192(C2xC4xC12).27C2192,489
(C2×C4×C12).28C2 = C4×Dic3⋊C4φ: C2/C1C2 ⊆ Aut C2×C4×C12192(C2xC4xC12).28C2192,490
(C2×C4×C12).29C2 = C426Dic3φ: C2/C1C2 ⊆ Aut C2×C4×C12192(C2xC4xC12).29C2192,491
(C2×C4×C12).30C2 = C3×C426C4φ: C2/C1C2 ⊆ Aut C2×C4×C1248(C2xC4xC12).30C2192,145
(C2×C4×C12).31C2 = C3×C428C4φ: C2/C1C2 ⊆ Aut C2×C4×C12192(C2xC4xC12).31C2192,815
(C2×C4×C12).32C2 = C3×C429C4φ: C2/C1C2 ⊆ Aut C2×C4×C12192(C2xC4xC12).32C2192,817
(C2×C4×C12).33C2 = C3×C23.65C23φ: C2/C1C2 ⊆ Aut C2×C4×C12192(C2xC4xC12).33C2192,822
(C2×C4×C12).34C2 = C3×C23.67C23φ: C2/C1C2 ⊆ Aut C2×C4×C12192(C2xC4xC12).34C2192,824
(C2×C4×C12).35C2 = C12×M4(2)φ: C2/C1C2 ⊆ Aut C2×C4×C1296(C2xC4xC12).35C2192,837
(C2×C4×C12).36C2 = C6×C4⋊C8φ: C2/C1C2 ⊆ Aut C2×C4×C12192(C2xC4xC12).36C2192,855
(C2×C4×C12).37C2 = C3×C4⋊M4(2)φ: C2/C1C2 ⊆ Aut C2×C4×C1296(C2xC4xC12).37C2192,856
(C2×C4×C12).38C2 = C3×C42.12C4φ: C2/C1C2 ⊆ Aut C2×C4×C1296(C2xC4xC12).38C2192,864
(C2×C4×C12).39C2 = C3×C42.6C4φ: C2/C1C2 ⊆ Aut C2×C4×C1296(C2xC4xC12).39C2192,865
(C2×C4×C12).40C2 = Q8×C2×C12φ: C2/C1C2 ⊆ Aut C2×C4×C12192(C2xC4xC12).40C2192,1405
(C2×C4×C12).41C2 = C6×C42.C2φ: C2/C1C2 ⊆ Aut C2×C4×C12192(C2xC4xC12).41C2192,1416
(C2×C4×C12).42C2 = C6×C4⋊Q8φ: C2/C1C2 ⊆ Aut C2×C4×C12192(C2xC4xC12).42C2192,1420
(C2×C4×C12).43C2 = C3×C23.37C23φ: C2/C1C2 ⊆ Aut C2×C4×C1296(C2xC4xC12).43C2192,1422

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