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

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

Semidirect products G=N:Q with N=C2×C3⋊S3 and Q=C2×C4
extensionφ:Q→Out NdρLabelID
(C2×C3⋊S3)⋊1(C2×C4) = Dic34D12φ: C2×C4/C2C22 ⊆ Out C2×C3⋊S348(C2xC3:S3):1(C2xC4)288,528
(C2×C3⋊S3)⋊2(C2×C4) = Dic35D12φ: C2×C4/C2C22 ⊆ Out C2×C3⋊S348(C2xC3:S3):2(C2xC4)288,542
(C2×C3⋊S3)⋊3(C2×C4) = C62.74C23φ: C2×C4/C2C22 ⊆ Out C2×C3⋊S348(C2xC3:S3):3(C2xC4)288,552
(C2×C3⋊S3)⋊4(C2×C4) = S3×D6⋊C4φ: C2×C4/C2C22 ⊆ Out C2×C3⋊S348(C2xC3:S3):4(C2xC4)288,568
(C2×C3⋊S3)⋊5(C2×C4) = C62.94C23φ: C2×C4/C2C22 ⊆ Out C2×C3⋊S348(C2xC3:S3):5(C2xC4)288,600
(C2×C3⋊S3)⋊6(C2×C4) = D4×C32⋊C4φ: C2×C4/C2C22 ⊆ Out C2×C3⋊S3248+(C2xC3:S3):6(C2xC4)288,936
(C2×C3⋊S3)⋊7(C2×C4) = C62.51C23φ: C2×C4/C4C2 ⊆ Out C2×C3⋊S348(C2xC3:S3):7(C2xC4)288,529
(C2×C3⋊S3)⋊8(C2×C4) = C4×C3⋊D12φ: C2×C4/C4C2 ⊆ Out C2×C3⋊S348(C2xC3:S3):8(C2xC4)288,551
(C2×C3⋊S3)⋊9(C2×C4) = C4×C12⋊S3φ: C2×C4/C4C2 ⊆ Out C2×C3⋊S3144(C2xC3:S3):9(C2xC4)288,730
(C2×C3⋊S3)⋊10(C2×C4) = C62.225C23φ: C2×C4/C4C2 ⊆ Out C2×C3⋊S3144(C2xC3:S3):10(C2xC4)288,738
(C2×C3⋊S3)⋊11(C2×C4) = C62.237C23φ: C2×C4/C4C2 ⊆ Out C2×C3⋊S3144(C2xC3:S3):11(C2xC4)288,750
(C2×C3⋊S3)⋊12(C2×C4) = C4×C327D4φ: C2×C4/C4C2 ⊆ Out C2×C3⋊S3144(C2xC3:S3):12(C2xC4)288,785
(C2×C3⋊S3)⋊13(C2×C4) = S32×C2×C4φ: C2×C4/C4C2 ⊆ Out C2×C3⋊S348(C2xC3:S3):13(C2xC4)288,950
(C2×C3⋊S3)⋊14(C2×C4) = C2×C6.D12φ: C2×C4/C22C2 ⊆ Out C2×C3⋊S348(C2xC3:S3):14(C2xC4)288,611
(C2×C3⋊S3)⋊15(C2×C4) = C62.116C23φ: C2×C4/C22C2 ⊆ Out C2×C3⋊S324(C2xC3:S3):15(C2xC4)288,622
(C2×C3⋊S3)⋊16(C2×C4) = C22⋊C4×C3⋊S3φ: C2×C4/C22C2 ⊆ Out C2×C3⋊S372(C2xC3:S3):16(C2xC4)288,737
(C2×C3⋊S3)⋊17(C2×C4) = C2×C6.11D12φ: C2×C4/C22C2 ⊆ Out C2×C3⋊S3144(C2xC3:S3):17(C2xC4)288,784
(C2×C3⋊S3)⋊18(C2×C4) = C2×C62⋊C4φ: C2×C4/C22C2 ⊆ Out C2×C3⋊S324(C2xC3:S3):18(C2xC4)288,941
(C2×C3⋊S3)⋊19(C2×C4) = C22×C6.D6φ: C2×C4/C22C2 ⊆ Out C2×C3⋊S348(C2xC3:S3):19(C2xC4)288,972
(C2×C3⋊S3)⋊20(C2×C4) = C23×C32⋊C4φ: C2×C4/C22C2 ⊆ Out C2×C3⋊S348(C2xC3:S3):20(C2xC4)288,1039

Non-split extensions G=N.Q with N=C2×C3⋊S3 and Q=C2×C4
extensionφ:Q→Out NdρLabelID
(C2×C3⋊S3).1(C2×C4) = C4×F9φ: C2×C4/C2C4 ⊆ Out C2×C3⋊S3368(C2xC3:S3).1(C2xC4)288,863
(C2×C3⋊S3).2(C2×C4) = C4⋊F9φ: C2×C4/C2C4 ⊆ Out C2×C3⋊S3368(C2xC3:S3).2(C2xC4)288,864
(C2×C3⋊S3).3(C2×C4) = C22⋊F9φ: C2×C4/C2C4 ⊆ Out C2×C3⋊S3248+(C2xC3:S3).3(C2xC4)288,867
(C2×C3⋊S3).4(C2×C4) = C22×F9φ: C2×C4/C2C4 ⊆ Out C2×C3⋊S336(C2xC3:S3).4(C2xC4)288,1030
(C2×C3⋊S3).5(C2×C4) = S32⋊C8φ: C2×C4/C2C22 ⊆ Out C2×C3⋊S3244(C2xC3:S3).5(C2xC4)288,374
(C2×C3⋊S3).6(C2×C4) = C4.S3≀C2φ: C2×C4/C2C22 ⊆ Out C2×C3⋊S3244(C2xC3:S3).6(C2xC4)288,375
(C2×C3⋊S3).7(C2×C4) = (C3×C12).D4φ: C2×C4/C2C22 ⊆ Out C2×C3⋊S3484(C2xC3:S3).7(C2xC4)288,376
(C2×C3⋊S3).8(C2×C4) = C32⋊C4⋊C8φ: C2×C4/C2C22 ⊆ Out C2×C3⋊S3484(C2xC3:S3).8(C2xC4)288,380
(C2×C3⋊S3).9(C2×C4) = C62.D4φ: C2×C4/C2C22 ⊆ Out C2×C3⋊S348(C2xC3:S3).9(C2xC4)288,385
(C2×C3⋊S3).10(C2×C4) = C62.2D4φ: C2×C4/C2C22 ⊆ Out C2×C3⋊S3244+(C2xC3:S3).10(C2xC4)288,386
(C2×C3⋊S3).11(C2×C4) = C4.4PSU3(𝔽2)φ: C2×C4/C2C22 ⊆ Out C2×C3⋊S3488(C2xC3:S3).11(C2xC4)288,392
(C2×C3⋊S3).12(C2×C4) = C62.Q8φ: C2×C4/C2C22 ⊆ Out C2×C3⋊S348(C2xC3:S3).12(C2xC4)288,395
(C2×C3⋊S3).13(C2×C4) = S3×C8⋊S3φ: C2×C4/C2C22 ⊆ Out C2×C3⋊S3484(C2xC3:S3).13(C2xC4)288,438
(C2×C3⋊S3).14(C2×C4) = C24.64D6φ: C2×C4/C2C22 ⊆ Out C2×C3⋊S3484(C2xC3:S3).14(C2xC4)288,452
(C2×C3⋊S3).15(C2×C4) = C3⋊C8.22D6φ: C2×C4/C2C22 ⊆ Out C2×C3⋊S3484(C2xC3:S3).15(C2xC4)288,465
(C2×C3⋊S3).16(C2×C4) = C62.6C23φ: C2×C4/C2C22 ⊆ Out C2×C3⋊S348(C2xC3:S3).16(C2xC4)288,484
(C2×C3⋊S3).17(C2×C4) = C2×S32⋊C4φ: C2×C4/C2C22 ⊆ Out C2×C3⋊S324(C2xC3:S3).17(C2xC4)288,880
(C2×C3⋊S3).18(C2×C4) = C2×C3⋊S3.Q8φ: C2×C4/C2C22 ⊆ Out C2×C3⋊S348(C2xC3:S3).18(C2xC4)288,882
(C2×C3⋊S3).19(C2×C4) = C2×C2.PSU3(𝔽2)φ: C2×C4/C2C22 ⊆ Out C2×C3⋊S348(C2xC3:S3).19(C2xC4)288,894
(C2×C3⋊S3).20(C2×C4) = C62.(C2×C4)φ: C2×C4/C2C22 ⊆ Out C2×C3⋊S3488-(C2xC3:S3).20(C2xC4)288,935
(C2×C3⋊S3).21(C2×C4) = C12⋊S3.C4φ: C2×C4/C2C22 ⊆ Out C2×C3⋊S3488+(C2xC3:S3).21(C2xC4)288,937
(C2×C3⋊S3).22(C2×C4) = C8×C32⋊C4φ: C2×C4/C4C2 ⊆ Out C2×C3⋊S3484(C2xC3:S3).22(C2xC4)288,414
(C2×C3⋊S3).23(C2×C4) = (C3×C24)⋊C4φ: C2×C4/C4C2 ⊆ Out C2×C3⋊S3484(C2xC3:S3).23(C2xC4)288,415
(C2×C3⋊S3).24(C2×C4) = (C6×C12)⋊2C4φ: C2×C4/C4C2 ⊆ Out C2×C3⋊S348(C2xC3:S3).24(C2xC4)288,429
(C2×C3⋊S3).25(C2×C4) = S32×C8φ: C2×C4/C4C2 ⊆ Out C2×C3⋊S3484(C2xC3:S3).25(C2xC4)288,437
(C2×C3⋊S3).26(C2×C4) = C24⋊D6φ: C2×C4/C4C2 ⊆ Out C2×C3⋊S3484(C2xC3:S3).26(C2xC4)288,439
(C2×C3⋊S3).27(C2×C4) = C24.63D6φ: C2×C4/C4C2 ⊆ Out C2×C3⋊S3484(C2xC3:S3).27(C2xC4)288,451
(C2×C3⋊S3).28(C2×C4) = C24.D6φ: C2×C4/C4C2 ⊆ Out C2×C3⋊S3484(C2xC3:S3).28(C2xC4)288,453
(C2×C3⋊S3).29(C2×C4) = C4×C6.D6φ: C2×C4/C4C2 ⊆ Out C2×C3⋊S348(C2xC3:S3).29(C2xC4)288,530
(C2×C3⋊S3).30(C2×C4) = C62.53C23φ: C2×C4/C4C2 ⊆ Out C2×C3⋊S348(C2xC3:S3).30(C2xC4)288,531
(C2×C3⋊S3).31(C2×C4) = C62.91C23φ: C2×C4/C4C2 ⊆ Out C2×C3⋊S348(C2xC3:S3).31(C2xC4)288,569
(C2×C3⋊S3).32(C2×C4) = C24.95D6φ: C2×C4/C4C2 ⊆ Out C2×C3⋊S3144(C2xC3:S3).32(C2xC4)288,758
(C2×C3⋊S3).33(C2×C4) = C24.47D6φ: C2×C4/C4C2 ⊆ Out C2×C3⋊S3144(C2xC3:S3).33(C2xC4)288,764
(C2×C3⋊S3).34(C2×C4) = C2×C12.29D6φ: C2×C4/C22C2 ⊆ Out C2×C3⋊S348(C2xC3:S3).34(C2xC4)288,464
(C2×C3⋊S3).35(C2×C4) = C3⋊C820D6φ: C2×C4/C22C2 ⊆ Out C2×C3⋊S3244(C2xC3:S3).35(C2xC4)288,466
(C2×C3⋊S3).36(C2×C4) = C2×C12.31D6φ: C2×C4/C22C2 ⊆ Out C2×C3⋊S348(C2xC3:S3).36(C2xC4)288,468
(C2×C3⋊S3).37(C2×C4) = C62.19C23φ: C2×C4/C22C2 ⊆ Out C2×C3⋊S348(C2xC3:S3).37(C2xC4)288,497
(C2×C3⋊S3).38(C2×C4) = C62.44C23φ: C2×C4/C22C2 ⊆ Out C2×C3⋊S348(C2xC3:S3).38(C2xC4)288,522
(C2×C3⋊S3).39(C2×C4) = C62.70C23φ: C2×C4/C22C2 ⊆ Out C2×C3⋊S348(C2xC3:S3).39(C2xC4)288,548
(C2×C3⋊S3).40(C2×C4) = C12216C2φ: C2×C4/C22C2 ⊆ Out C2×C3⋊S3144(C2xC3:S3).40(C2xC4)288,729
(C2×C3⋊S3).41(C2×C4) = C62.236C23φ: C2×C4/C22C2 ⊆ Out C2×C3⋊S3144(C2xC3:S3).41(C2xC4)288,749
(C2×C3⋊S3).42(C2×C4) = C2×C24⋊S3φ: C2×C4/C22C2 ⊆ Out C2×C3⋊S3144(C2xC3:S3).42(C2xC4)288,757
(C2×C3⋊S3).43(C2×C4) = M4(2)×C3⋊S3φ: C2×C4/C22C2 ⊆ Out C2×C3⋊S372(C2xC3:S3).43(C2xC4)288,763
(C2×C3⋊S3).44(C2×C4) = C2×C3⋊S33C8φ: C2×C4/C22C2 ⊆ Out C2×C3⋊S348(C2xC3:S3).44(C2xC4)288,929
(C2×C3⋊S3).45(C2×C4) = C2×C32⋊M4(2)φ: C2×C4/C22C2 ⊆ Out C2×C3⋊S348(C2xC3:S3).45(C2xC4)288,930
(C2×C3⋊S3).46(C2×C4) = C3⋊S3⋊M4(2)φ: C2×C4/C22C2 ⊆ Out C2×C3⋊S3244(C2xC3:S3).46(C2xC4)288,931
(C2×C3⋊S3).47(C2×C4) = C2×C4×C32⋊C4φ: C2×C4/C22C2 ⊆ Out C2×C3⋊S348(C2xC3:S3).47(C2xC4)288,932
(C2×C3⋊S3).48(C2×C4) = C2×C4⋊(C32⋊C4)φ: C2×C4/C22C2 ⊆ Out C2×C3⋊S348(C2xC3:S3).48(C2xC4)288,933
(C2×C3⋊S3).49(C2×C4) = (C6×C12)⋊5C4φ: C2×C4/C22C2 ⊆ Out C2×C3⋊S3244(C2xC3:S3).49(C2xC4)288,934
(C2×C3⋊S3).50(C2×C4) = C42×C3⋊S3φ: trivial image144(C2xC3:S3).50(C2xC4)288,728
(C2×C3⋊S3).51(C2×C4) = C4⋊C4×C3⋊S3φ: trivial image144(C2xC3:S3).51(C2xC4)288,748
(C2×C3⋊S3).52(C2×C4) = C2×C8×C3⋊S3φ: trivial image144(C2xC3:S3).52(C2xC4)288,756

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