# Extensions 1→N→G→Q→1 with N=C2×C4×C3⋊S3 and Q=C2

Direct product G=N×Q with N=C2×C4×C3⋊S3 and Q=C2
dρLabelID
C22×C4×C3⋊S3144C2^2xC4xC3:S3288,1004

Semidirect products G=N:Q with N=C2×C4×C3⋊S3 and Q=C2
extensionφ:Q→Out NdρLabelID
(C2×C4×C3⋊S3)⋊1C2 = C122D12φ: C2/C1C2 ⊆ Out C2×C4×C3⋊S348(C2xC4xC3:S3):1C2288,564
(C2×C4×C3⋊S3)⋊2C2 = C123D12φ: C2/C1C2 ⊆ Out C2×C4×C3⋊S3144(C2xC4xC3:S3):2C2288,752
(C2×C4×C3⋊S3)⋊3C2 = C62.256C23φ: C2/C1C2 ⊆ Out C2×C4×C3⋊S3144(C2xC4xC3:S3):3C2288,795
(C2×C4×C3⋊S3)⋊4C2 = C2×D12⋊S3φ: C2/C1C2 ⊆ Out C2×C4×C3⋊S348(C2xC4xC3:S3):4C2288,944
(C2×C4×C3⋊S3)⋊5C2 = C2×D6⋊D6φ: C2/C1C2 ⊆ Out C2×C4×C3⋊S348(C2xC4xC3:S3):5C2288,952
(C2×C4×C3⋊S3)⋊6C2 = D1223D6φ: C2/C1C2 ⊆ Out C2×C4×C3⋊S3244(C2xC4xC3:S3):6C2288,954
(C2×C4×C3⋊S3)⋊7C2 = C2×D4×C3⋊S3φ: C2/C1C2 ⊆ Out C2×C4×C3⋊S372(C2xC4xC3:S3):7C2288,1007
(C2×C4×C3⋊S3)⋊8C2 = C2×C12.D6φ: C2/C1C2 ⊆ Out C2×C4×C3⋊S3144(C2xC4xC3:S3):8C2288,1008
(C2×C4×C3⋊S3)⋊9C2 = C2×C12.26D6φ: C2/C1C2 ⊆ Out C2×C4×C3⋊S3144(C2xC4xC3:S3):9C2288,1011
(C2×C4×C3⋊S3)⋊10C2 = C4○D4×C3⋊S3φ: C2/C1C2 ⊆ Out C2×C4×C3⋊S372(C2xC4xC3:S3):10C2288,1013
(C2×C4×C3⋊S3)⋊11C2 = C62.23C23φ: C2/C1C2 ⊆ Out C2×C4×C3⋊S348(C2xC4xC3:S3):11C2288,501
(C2×C4×C3⋊S3)⋊12C2 = C62.51C23φ: C2/C1C2 ⊆ Out C2×C4×C3⋊S348(C2xC4xC3:S3):12C2288,529
(C2×C4×C3⋊S3)⋊13C2 = C4×C3⋊D12φ: C2/C1C2 ⊆ Out C2×C4×C3⋊S348(C2xC4xC3:S3):13C2288,551
(C2×C4×C3⋊S3)⋊14C2 = C62.82C23φ: C2/C1C2 ⊆ Out C2×C4×C3⋊S348(C2xC4xC3:S3):14C2288,560
(C2×C4×C3⋊S3)⋊15C2 = C62.91C23φ: C2/C1C2 ⊆ Out C2×C4×C3⋊S348(C2xC4xC3:S3):15C2288,569
(C2×C4×C3⋊S3)⋊16C2 = C4×C12⋊S3φ: C2/C1C2 ⊆ Out C2×C4×C3⋊S3144(C2xC4xC3:S3):16C2288,730
(C2×C4×C3⋊S3)⋊17C2 = C22⋊C4×C3⋊S3φ: C2/C1C2 ⊆ Out C2×C4×C3⋊S372(C2xC4xC3:S3):17C2288,737
(C2×C4×C3⋊S3)⋊18C2 = C62.225C23φ: C2/C1C2 ⊆ Out C2×C4×C3⋊S3144(C2xC4xC3:S3):18C2288,738
(C2×C4×C3⋊S3)⋊19C2 = C62.227C23φ: C2/C1C2 ⊆ Out C2×C4×C3⋊S3144(C2xC4xC3:S3):19C2288,740
(C2×C4×C3⋊S3)⋊20C2 = C62.228C23φ: C2/C1C2 ⊆ Out C2×C4×C3⋊S3144(C2xC4xC3:S3):20C2288,741
(C2×C4×C3⋊S3)⋊21C2 = C62.237C23φ: C2/C1C2 ⊆ Out C2×C4×C3⋊S3144(C2xC4xC3:S3):21C2288,750
(C2×C4×C3⋊S3)⋊22C2 = C62.238C23φ: C2/C1C2 ⊆ Out C2×C4×C3⋊S3144(C2xC4xC3:S3):22C2288,751
(C2×C4×C3⋊S3)⋊23C2 = C4×C327D4φ: C2/C1C2 ⊆ Out C2×C4×C3⋊S3144(C2xC4xC3:S3):23C2288,785
(C2×C4×C3⋊S3)⋊24C2 = C2×D6.D6φ: C2/C1C2 ⊆ Out C2×C4×C3⋊S348(C2xC4xC3:S3):24C2288,948
(C2×C4×C3⋊S3)⋊25C2 = S32×C2×C4φ: C2/C1C2 ⊆ Out C2×C4×C3⋊S348(C2xC4xC3:S3):25C2288,950
(C2×C4×C3⋊S3)⋊26C2 = C2×C12.59D6φ: C2/C1C2 ⊆ Out C2×C4×C3⋊S3144(C2xC4xC3:S3):26C2288,1006

Non-split extensions G=N.Q with N=C2×C4×C3⋊S3 and Q=C2
extensionφ:Q→Out NdρLabelID
(C2×C4×C3⋊S3).1C2 = C3⋊C820D6φ: C2/C1C2 ⊆ Out C2×C4×C3⋊S3244(C2xC4xC3:S3).1C2288,466
(C2×C4×C3⋊S3).2C2 = C62.19C23φ: C2/C1C2 ⊆ Out C2×C4×C3⋊S348(C2xC4xC3:S3).2C2288,497
(C2×C4×C3⋊S3).3C2 = C12.30D12φ: C2/C1C2 ⊆ Out C2×C4×C3⋊S348(C2xC4xC3:S3).3C2288,519
(C2×C4×C3⋊S3).4C2 = C62.70C23φ: C2/C1C2 ⊆ Out C2×C4×C3⋊S348(C2xC4xC3:S3).4C2288,548
(C2×C4×C3⋊S3).5C2 = C62.236C23φ: C2/C1C2 ⊆ Out C2×C4×C3⋊S3144(C2xC4xC3:S3).5C2288,749
(C2×C4×C3⋊S3).6C2 = C12.31D12φ: C2/C1C2 ⊆ Out C2×C4×C3⋊S3144(C2xC4xC3:S3).6C2288,754
(C2×C4×C3⋊S3).7C2 = M4(2)×C3⋊S3φ: C2/C1C2 ⊆ Out C2×C4×C3⋊S372(C2xC4xC3:S3).7C2288,763
(C2×C4×C3⋊S3).8C2 = C62.261C23φ: C2/C1C2 ⊆ Out C2×C4×C3⋊S3144(C2xC4xC3:S3).8C2288,803
(C2×C4×C3⋊S3).9C2 = C2×Dic3.D6φ: C2/C1C2 ⊆ Out C2×C4×C3⋊S348(C2xC4xC3:S3).9C2288,947
(C2×C4×C3⋊S3).10C2 = C2×Q8×C3⋊S3φ: C2/C1C2 ⊆ Out C2×C4×C3⋊S3144(C2xC4xC3:S3).10C2288,1010
(C2×C4×C3⋊S3).11C2 = C12.78D12φ: C2/C1C2 ⊆ Out C2×C4×C3⋊S348(C2xC4xC3:S3).11C2288,205
(C2×C4×C3⋊S3).12C2 = C12.60D12φ: C2/C1C2 ⊆ Out C2×C4×C3⋊S3144(C2xC4xC3:S3).12C2288,295
(C2×C4×C3⋊S3).13C2 = C62.6(C2×C4)φ: C2/C1C2 ⊆ Out C2×C4×C3⋊S348(C2xC4xC3:S3).13C2288,426
(C2×C4×C3⋊S3).14C2 = (C6×C12)⋊2C4φ: C2/C1C2 ⊆ Out C2×C4×C3⋊S348(C2xC4xC3:S3).14C2288,429
(C2×C4×C3⋊S3).15C2 = C2×C12.29D6φ: C2/C1C2 ⊆ Out C2×C4×C3⋊S348(C2xC4xC3:S3).15C2288,464
(C2×C4×C3⋊S3).16C2 = C2×C12.31D6φ: C2/C1C2 ⊆ Out C2×C4×C3⋊S348(C2xC4xC3:S3).16C2288,468
(C2×C4×C3⋊S3).17C2 = C62.35C23φ: C2/C1C2 ⊆ Out C2×C4×C3⋊S348(C2xC4xC3:S3).17C2288,513
(C2×C4×C3⋊S3).18C2 = C62.44C23φ: C2/C1C2 ⊆ Out C2×C4×C3⋊S348(C2xC4xC3:S3).18C2288,522
(C2×C4×C3⋊S3).19C2 = C4×C6.D6φ: C2/C1C2 ⊆ Out C2×C4×C3⋊S348(C2xC4xC3:S3).19C2288,530
(C2×C4×C3⋊S3).20C2 = C62.53C23φ: C2/C1C2 ⊆ Out C2×C4×C3⋊S348(C2xC4xC3:S3).20C2288,531
(C2×C4×C3⋊S3).21C2 = C12216C2φ: C2/C1C2 ⊆ Out C2×C4×C3⋊S3144(C2xC4xC3:S3).21C2288,729
(C2×C4×C3⋊S3).22C2 = C4⋊C4×C3⋊S3φ: C2/C1C2 ⊆ Out C2×C4×C3⋊S3144(C2xC4xC3:S3).22C2288,748
(C2×C4×C3⋊S3).23C2 = C62.240C23φ: C2/C1C2 ⊆ Out C2×C4×C3⋊S3144(C2xC4xC3:S3).23C2288,753
(C2×C4×C3⋊S3).24C2 = C2×C24⋊S3φ: C2/C1C2 ⊆ Out C2×C4×C3⋊S3144(C2xC4xC3:S3).24C2288,757
(C2×C4×C3⋊S3).25C2 = C2×C3⋊S33C8φ: C2/C1C2 ⊆ Out C2×C4×C3⋊S348(C2xC4xC3:S3).25C2288,929
(C2×C4×C3⋊S3).26C2 = C2×C32⋊M4(2)φ: C2/C1C2 ⊆ Out C2×C4×C3⋊S348(C2xC4xC3:S3).26C2288,930
(C2×C4×C3⋊S3).27C2 = C3⋊S3⋊M4(2)φ: C2/C1C2 ⊆ Out C2×C4×C3⋊S3244(C2xC4xC3:S3).27C2288,931
(C2×C4×C3⋊S3).28C2 = C2×C4×C32⋊C4φ: C2/C1C2 ⊆ Out C2×C4×C3⋊S348(C2xC4xC3:S3).28C2288,932
(C2×C4×C3⋊S3).29C2 = C2×C4⋊(C32⋊C4)φ: C2/C1C2 ⊆ Out C2×C4×C3⋊S348(C2xC4xC3:S3).29C2288,933
(C2×C4×C3⋊S3).30C2 = (C6×C12)⋊5C4φ: C2/C1C2 ⊆ Out C2×C4×C3⋊S3244(C2xC4xC3:S3).30C2288,934
(C2×C4×C3⋊S3).31C2 = C42×C3⋊S3φ: trivial image144(C2xC4xC3:S3).31C2288,728
(C2×C4×C3⋊S3).32C2 = C2×C8×C3⋊S3φ: trivial image144(C2xC4xC3:S3).32C2288,756

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