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Extensions 1→N→G→Q→1 with N=C6 and Q=S3×C2×C4

Direct product G=N×Q with N=C6 and Q=S3×C2×C4
dρLabelID
S3×C22×C1296S3xC2^2xC12288,989

Semidirect products G=N:Q with N=C6 and Q=S3×C2×C4
extensionφ:Q→Aut NdρLabelID
C6⋊1(S3×C2×C4) = S32×C2×C4φ: S3×C2×C4/C4×S3 → C2 ⊆ Aut C648C6:1(S3xC2xC4)288,950
C6⋊2(S3×C2×C4) = C22×C6.D6φ: S3×C2×C4/C2×Dic3 → C2 ⊆ Aut C648C6:2(S3xC2xC4)288,972
C6⋊3(S3×C2×C4) = C22×C4×C3⋊S3φ: S3×C2×C4/C2×C12 → C2 ⊆ Aut C6144C6:3(S3xC2xC4)288,1004
C6⋊4(S3×C2×C4) = C22×S3×Dic3φ: S3×C2×C4/C22×S3 → C2 ⊆ Aut C696C6:4(S3xC2xC4)288,969

Non-split extensions G=N.Q with N=C6 and Q=S3×C2×C4
extensionφ:Q→Aut NdρLabelID
C6.1(S3×C2×C4) = S32×C8φ: S3×C2×C4/C4×S3 → C2 ⊆ Aut C6484C6.1(S3xC2xC4)288,437
C6.2(S3×C2×C4) = S3×C8⋊S3φ: S3×C2×C4/C4×S3 → C2 ⊆ Aut C6484C6.2(S3xC2xC4)288,438
C6.3(S3×C2×C4) = C24⋊D6φ: S3×C2×C4/C4×S3 → C2 ⊆ Aut C6484C6.3(S3xC2xC4)288,439
C6.4(S3×C2×C4) = C24.63D6φ: S3×C2×C4/C4×S3 → C2 ⊆ Aut C6484C6.4(S3xC2xC4)288,451
C6.5(S3×C2×C4) = C24.64D6φ: S3×C2×C4/C4×S3 → C2 ⊆ Aut C6484C6.5(S3xC2xC4)288,452
C6.6(S3×C2×C4) = C24.D6φ: S3×C2×C4/C4×S3 → C2 ⊆ Aut C6484C6.6(S3xC2xC4)288,453
C6.7(S3×C2×C4) = C62.6C23φ: S3×C2×C4/C4×S3 → C2 ⊆ Aut C648C6.7(S3xC2xC4)288,484
C6.8(S3×C2×C4) = Dic3⋊5Dic6φ: S3×C2×C4/C4×S3 → C2 ⊆ Aut C696C6.8(S3xC2xC4)288,485
C6.9(S3×C2×C4) = C62.8C23φ: S3×C2×C4/C4×S3 → C2 ⊆ Aut C696C6.9(S3xC2xC4)288,486
C6.10(S3×C2×C4) = C4×S3×Dic3φ: S3×C2×C4/C4×S3 → C2 ⊆ Aut C696C6.10(S3xC2xC4)288,523
C6.11(S3×C2×C4) = S3×Dic3⋊C4φ: S3×C2×C4/C4×S3 → C2 ⊆ Aut C696C6.11(S3xC2xC4)288,524
C6.12(S3×C2×C4) = C62.47C23φ: S3×C2×C4/C4×S3 → C2 ⊆ Aut C696C6.12(S3xC2xC4)288,525
C6.13(S3×C2×C4) = C62.48C23φ: S3×C2×C4/C4×S3 → C2 ⊆ Aut C696C6.13(S3xC2xC4)288,526
C6.14(S3×C2×C4) = C62.49C23φ: S3×C2×C4/C4×S3 → C2 ⊆ Aut C696C6.14(S3xC2xC4)288,527
C6.15(S3×C2×C4) = Dic3⋊4D12φ: S3×C2×C4/C4×S3 → C2 ⊆ Aut C648C6.15(S3xC2xC4)288,528
C6.16(S3×C2×C4) = C62.51C23φ: S3×C2×C4/C4×S3 → C2 ⊆ Aut C648C6.16(S3xC2xC4)288,529
C6.17(S3×C2×C4) = C62.53C23φ: S3×C2×C4/C4×S3 → C2 ⊆ Aut C648C6.17(S3xC2xC4)288,531
C6.18(S3×C2×C4) = C4×D6⋊S3φ: S3×C2×C4/C4×S3 → C2 ⊆ Aut C696C6.18(S3xC2xC4)288,549
C6.19(S3×C2×C4) = C62.72C23φ: S3×C2×C4/C4×S3 → C2 ⊆ Aut C696C6.19(S3xC2xC4)288,550
C6.20(S3×C2×C4) = C4×C3⋊D12φ: S3×C2×C4/C4×S3 → C2 ⊆ Aut C648C6.20(S3xC2xC4)288,551
C6.21(S3×C2×C4) = C62.74C23φ: S3×C2×C4/C4×S3 → C2 ⊆ Aut C648C6.21(S3xC2xC4)288,552
C6.22(S3×C2×C4) = C4×C32⋊2Q8φ: S3×C2×C4/C4×S3 → C2 ⊆ Aut C696C6.22(S3xC2xC4)288,565
C6.23(S3×C2×C4) = S3×D6⋊C4φ: S3×C2×C4/C4×S3 → C2 ⊆ Aut C648C6.23(S3xC2xC4)288,568
C6.24(S3×C2×C4) = C62.91C23φ: S3×C2×C4/C4×S3 → C2 ⊆ Aut C648C6.24(S3xC2xC4)288,569
C6.25(S3×C2×C4) = C2×C12.29D6φ: S3×C2×C4/C2×Dic3 → C2 ⊆ Aut C648C6.25(S3xC2xC4)288,464
C6.26(S3×C2×C4) = C3⋊C8.22D6φ: S3×C2×C4/C2×Dic3 → C2 ⊆ Aut C6484C6.26(S3xC2xC4)288,465
C6.27(S3×C2×C4) = C3⋊C8⋊20D6φ: S3×C2×C4/C2×Dic3 → C2 ⊆ Aut C6244C6.27(S3xC2xC4)288,466
C6.28(S3×C2×C4) = C2×C12.31D6φ: S3×C2×C4/C2×Dic3 → C2 ⊆ Aut C648C6.28(S3xC2xC4)288,468
C6.29(S3×C2×C4) = Dic3⋊6Dic6φ: S3×C2×C4/C2×Dic3 → C2 ⊆ Aut C696C6.29(S3xC2xC4)288,492
C6.30(S3×C2×C4) = C62.19C23φ: S3×C2×C4/C2×Dic3 → C2 ⊆ Aut C648C6.30(S3xC2xC4)288,497
C6.31(S3×C2×C4) = C62.44C23φ: S3×C2×C4/C2×Dic3 → C2 ⊆ Aut C648C6.31(S3xC2xC4)288,522
C6.32(S3×C2×C4) = C4×C6.D6φ: S3×C2×C4/C2×Dic3 → C2 ⊆ Aut C648C6.32(S3xC2xC4)288,530
C6.33(S3×C2×C4) = Dic3⋊5D12φ: S3×C2×C4/C2×Dic3 → C2 ⊆ Aut C648C6.33(S3xC2xC4)288,542
C6.34(S3×C2×C4) = C62.70C23φ: S3×C2×C4/C2×Dic3 → C2 ⊆ Aut C648C6.34(S3xC2xC4)288,548
C6.35(S3×C2×C4) = C62.94C23φ: S3×C2×C4/C2×Dic3 → C2 ⊆ Aut C648C6.35(S3xC2xC4)288,600
C6.36(S3×C2×C4) = C62.99C23φ: S3×C2×C4/C2×Dic3 → C2 ⊆ Aut C648C6.36(S3xC2xC4)288,605
C6.37(S3×C2×C4) = C2×C6.D12φ: S3×C2×C4/C2×Dic3 → C2 ⊆ Aut C648C6.37(S3xC2xC4)288,611
C6.38(S3×C2×C4) = C2×C62.C22φ: S3×C2×C4/C2×Dic3 → C2 ⊆ Aut C696C6.38(S3xC2xC4)288,615
C6.39(S3×C2×C4) = C62.116C23φ: S3×C2×C4/C2×Dic3 → C2 ⊆ Aut C624C6.39(S3xC2xC4)288,622
C6.40(S3×C2×C4) = C4×Dic18φ: S3×C2×C4/C2×C12 → C2 ⊆ Aut C6288C6.40(S3xC2xC4)288,78
C6.41(S3×C2×C4) = C42×D9φ: S3×C2×C4/C2×C12 → C2 ⊆ Aut C6144C6.41(S3xC2xC4)288,81
C6.42(S3×C2×C4) = C42⋊2D9φ: S3×C2×C4/C2×C12 → C2 ⊆ Aut C6144C6.42(S3xC2xC4)288,82
C6.43(S3×C2×C4) = C4×D36φ: S3×C2×C4/C2×C12 → C2 ⊆ Aut C6144C6.43(S3xC2xC4)288,83
C6.44(S3×C2×C4) = C23.16D18φ: S3×C2×C4/C2×C12 → C2 ⊆ Aut C6144C6.44(S3xC2xC4)288,87
C6.45(S3×C2×C4) = C22⋊C4×D9φ: S3×C2×C4/C2×C12 → C2 ⊆ Aut C672C6.45(S3xC2xC4)288,90
C6.46(S3×C2×C4) = Dic9⋊4D4φ: S3×C2×C4/C2×C12 → C2 ⊆ Aut C6144C6.46(S3xC2xC4)288,91
C6.47(S3×C2×C4) = Dic9⋊3Q8φ: S3×C2×C4/C2×C12 → C2 ⊆ Aut C6288C6.47(S3xC2xC4)288,97
C6.48(S3×C2×C4) = C4⋊C4×D9φ: S3×C2×C4/C2×C12 → C2 ⊆ Aut C6144C6.48(S3xC2xC4)288,101
C6.49(S3×C2×C4) = C4⋊C4⋊7D9φ: S3×C2×C4/C2×C12 → C2 ⊆ Aut C6144C6.49(S3xC2xC4)288,102
C6.50(S3×C2×C4) = D36⋊C4φ: S3×C2×C4/C2×C12 → C2 ⊆ Aut C6144C6.50(S3xC2xC4)288,103
C6.51(S3×C2×C4) = C2×C8×D9φ: S3×C2×C4/C2×C12 → C2 ⊆ Aut C6144C6.51(S3xC2xC4)288,110
C6.52(S3×C2×C4) = C2×C8⋊D9φ: S3×C2×C4/C2×C12 → C2 ⊆ Aut C6144C6.52(S3xC2xC4)288,111
C6.53(S3×C2×C4) = D36.2C4φ: S3×C2×C4/C2×C12 → C2 ⊆ Aut C61442C6.53(S3xC2xC4)288,112
C6.54(S3×C2×C4) = M4(2)×D9φ: S3×C2×C4/C2×C12 → C2 ⊆ Aut C6724C6.54(S3xC2xC4)288,116
C6.55(S3×C2×C4) = D36.C4φ: S3×C2×C4/C2×C12 → C2 ⊆ Aut C61444C6.55(S3xC2xC4)288,117
C6.56(S3×C2×C4) = C2×C4×Dic9φ: S3×C2×C4/C2×C12 → C2 ⊆ Aut C6288C6.56(S3xC2xC4)288,132
C6.57(S3×C2×C4) = C2×Dic9⋊C4φ: S3×C2×C4/C2×C12 → C2 ⊆ Aut C6288C6.57(S3xC2xC4)288,133
C6.58(S3×C2×C4) = C2×D18⋊C4φ: S3×C2×C4/C2×C12 → C2 ⊆ Aut C6144C6.58(S3xC2xC4)288,137
C6.59(S3×C2×C4) = C4×C9⋊D4φ: S3×C2×C4/C2×C12 → C2 ⊆ Aut C6144C6.59(S3xC2xC4)288,138
C6.60(S3×C2×C4) = C22×C4×D9φ: S3×C2×C4/C2×C12 → C2 ⊆ Aut C6144C6.60(S3xC2xC4)288,353
C6.61(S3×C2×C4) = C4×C32⋊4Q8φ: S3×C2×C4/C2×C12 → C2 ⊆ Aut C6288C6.61(S3xC2xC4)288,725
C6.62(S3×C2×C4) = C42×C3⋊S3φ: S3×C2×C4/C2×C12 → C2 ⊆ Aut C6144C6.62(S3xC2xC4)288,728
C6.63(S3×C2×C4) = C122⋊16C2φ: S3×C2×C4/C2×C12 → C2 ⊆ Aut C6144C6.63(S3xC2xC4)288,729
C6.64(S3×C2×C4) = C4×C12⋊S3φ: S3×C2×C4/C2×C12 → C2 ⊆ Aut C6144C6.64(S3xC2xC4)288,730
C6.65(S3×C2×C4) = C62.221C23φ: S3×C2×C4/C2×C12 → C2 ⊆ Aut C6144C6.65(S3xC2xC4)288,734
C6.66(S3×C2×C4) = C22⋊C4×C3⋊S3φ: S3×C2×C4/C2×C12 → C2 ⊆ Aut C672C6.66(S3xC2xC4)288,737
C6.67(S3×C2×C4) = C62.225C23φ: S3×C2×C4/C2×C12 → C2 ⊆ Aut C6144C6.67(S3xC2xC4)288,738
C6.68(S3×C2×C4) = C62.231C23φ: S3×C2×C4/C2×C12 → C2 ⊆ Aut C6288C6.68(S3xC2xC4)288,744
C6.69(S3×C2×C4) = C4⋊C4×C3⋊S3φ: S3×C2×C4/C2×C12 → C2 ⊆ Aut C6144C6.69(S3xC2xC4)288,748
C6.70(S3×C2×C4) = C62.236C23φ: S3×C2×C4/C2×C12 → C2 ⊆ Aut C6144C6.70(S3xC2xC4)288,749
C6.71(S3×C2×C4) = C62.237C23φ: S3×C2×C4/C2×C12 → C2 ⊆ Aut C6144C6.71(S3xC2xC4)288,750
C6.72(S3×C2×C4) = C2×C8×C3⋊S3φ: S3×C2×C4/C2×C12 → C2 ⊆ Aut C6144C6.72(S3xC2xC4)288,756
C6.73(S3×C2×C4) = C2×C24⋊S3φ: S3×C2×C4/C2×C12 → C2 ⊆ Aut C6144C6.73(S3xC2xC4)288,757
C6.74(S3×C2×C4) = C24.95D6φ: S3×C2×C4/C2×C12 → C2 ⊆ Aut C6144C6.74(S3xC2xC4)288,758
C6.75(S3×C2×C4) = M4(2)×C3⋊S3φ: S3×C2×C4/C2×C12 → C2 ⊆ Aut C672C6.75(S3xC2xC4)288,763
C6.76(S3×C2×C4) = C24.47D6φ: S3×C2×C4/C2×C12 → C2 ⊆ Aut C6144C6.76(S3xC2xC4)288,764
C6.77(S3×C2×C4) = C2×C4×C3⋊Dic3φ: S3×C2×C4/C2×C12 → C2 ⊆ Aut C6288C6.77(S3xC2xC4)288,779
C6.78(S3×C2×C4) = C2×C6.Dic6φ: S3×C2×C4/C2×C12 → C2 ⊆ Aut C6288C6.78(S3xC2xC4)288,780
C6.79(S3×C2×C4) = C2×C6.11D12φ: S3×C2×C4/C2×C12 → C2 ⊆ Aut C6144C6.79(S3xC2xC4)288,784
C6.80(S3×C2×C4) = C4×C32⋊7D4φ: S3×C2×C4/C2×C12 → C2 ⊆ Aut C6144C6.80(S3xC2xC4)288,785
C6.81(S3×C2×C4) = C2×S3×C3⋊C8φ: S3×C2×C4/C22×S3 → C2 ⊆ Aut C696C6.81(S3xC2xC4)288,460
C6.82(S3×C2×C4) = S3×C4.Dic3φ: S3×C2×C4/C22×S3 → C2 ⊆ Aut C6484C6.82(S3xC2xC4)288,461
C6.83(S3×C2×C4) = D12.2Dic3φ: S3×C2×C4/C22×S3 → C2 ⊆ Aut C6484C6.83(S3xC2xC4)288,462
C6.84(S3×C2×C4) = D12.Dic3φ: S3×C2×C4/C22×S3 → C2 ⊆ Aut C6484C6.84(S3xC2xC4)288,463
C6.85(S3×C2×C4) = C2×D6.Dic3φ: S3×C2×C4/C22×S3 → C2 ⊆ Aut C696C6.85(S3xC2xC4)288,467
C6.86(S3×C2×C4) = C62.11C23φ: S3×C2×C4/C22×S3 → C2 ⊆ Aut C696C6.86(S3xC2xC4)288,489
C6.87(S3×C2×C4) = Dic3×Dic6φ: S3×C2×C4/C22×S3 → C2 ⊆ Aut C696C6.87(S3xC2xC4)288,490
C6.88(S3×C2×C4) = C62.13C23φ: S3×C2×C4/C22×S3 → C2 ⊆ Aut C696C6.88(S3xC2xC4)288,491
C6.89(S3×C2×C4) = C62.25C23φ: S3×C2×C4/C22×S3 → C2 ⊆ Aut C696C6.89(S3xC2xC4)288,503
C6.90(S3×C2×C4) = S3×C4⋊Dic3φ: S3×C2×C4/C22×S3 → C2 ⊆ Aut C696C6.90(S3xC2xC4)288,537
C6.91(S3×C2×C4) = Dic3×D12φ: S3×C2×C4/C22×S3 → C2 ⊆ Aut C696C6.91(S3xC2xC4)288,540
C6.92(S3×C2×C4) = D12⋊Dic3φ: S3×C2×C4/C22×S3 → C2 ⊆ Aut C696C6.92(S3xC2xC4)288,546
C6.93(S3×C2×C4) = C2×Dic32φ: S3×C2×C4/C22×S3 → C2 ⊆ Aut C696C6.93(S3xC2xC4)288,602
C6.94(S3×C2×C4) = C62.97C23φ: S3×C2×C4/C22×S3 → C2 ⊆ Aut C648C6.94(S3xC2xC4)288,603
C6.95(S3×C2×C4) = C2×D6⋊Dic3φ: S3×C2×C4/C22×S3 → C2 ⊆ Aut C696C6.95(S3xC2xC4)288,608
C6.96(S3×C2×C4) = C2×Dic3⋊Dic3φ: S3×C2×C4/C22×S3 → C2 ⊆ Aut C696C6.96(S3xC2xC4)288,613
C6.97(S3×C2×C4) = S3×C6.D4φ: S3×C2×C4/C22×S3 → C2 ⊆ Aut C648C6.97(S3xC2xC4)288,616
C6.98(S3×C2×C4) = Dic3×C3⋊D4φ: S3×C2×C4/C22×S3 → C2 ⊆ Aut C648C6.98(S3xC2xC4)288,620
C6.99(S3×C2×C4) = C62.115C23φ: S3×C2×C4/C22×S3 → C2 ⊆ Aut C648C6.99(S3xC2xC4)288,621
C6.100(S3×C2×C4) = C12×Dic6central extension (φ=1)96C6.100(S3xC2xC4)288,639
C6.101(S3×C2×C4) = S3×C4×C12central extension (φ=1)96C6.101(S3xC2xC4)288,642
C6.102(S3×C2×C4) = C3×C42⋊2S3central extension (φ=1)96C6.102(S3xC2xC4)288,643
C6.103(S3×C2×C4) = C12×D12central extension (φ=1)96C6.103(S3xC2xC4)288,644
C6.104(S3×C2×C4) = C3×C23.16D6central extension (φ=1)48C6.104(S3xC2xC4)288,648
C6.105(S3×C2×C4) = C3×S3×C22⋊C4central extension (φ=1)48C6.105(S3xC2xC4)288,651
C6.106(S3×C2×C4) = C3×Dic3⋊4D4central extension (φ=1)48C6.106(S3xC2xC4)288,652
C6.107(S3×C2×C4) = C3×Dic6⋊C4central extension (φ=1)96C6.107(S3xC2xC4)288,658
C6.108(S3×C2×C4) = C3×S3×C4⋊C4central extension (φ=1)96C6.108(S3xC2xC4)288,662
C6.109(S3×C2×C4) = C3×C4⋊C4⋊7S3central extension (φ=1)96C6.109(S3xC2xC4)288,663
C6.110(S3×C2×C4) = C3×Dic3⋊5D4central extension (φ=1)96C6.110(S3xC2xC4)288,664
C6.111(S3×C2×C4) = S3×C2×C24central extension (φ=1)96C6.111(S3xC2xC4)288,670
C6.112(S3×C2×C4) = C6×C8⋊S3central extension (φ=1)96C6.112(S3xC2xC4)288,671
C6.113(S3×C2×C4) = C3×C8○D12central extension (φ=1)482C6.113(S3xC2xC4)288,672
C6.114(S3×C2×C4) = C3×S3×M4(2)central extension (φ=1)484C6.114(S3xC2xC4)288,677
C6.115(S3×C2×C4) = C3×D12.C4central extension (φ=1)484C6.115(S3xC2xC4)288,678
C6.116(S3×C2×C4) = Dic3×C2×C12central extension (φ=1)96C6.116(S3xC2xC4)288,693
C6.117(S3×C2×C4) = C6×Dic3⋊C4central extension (φ=1)96C6.117(S3xC2xC4)288,694
C6.118(S3×C2×C4) = C6×D6⋊C4central extension (φ=1)96C6.118(S3xC2xC4)288,698
C6.119(S3×C2×C4) = C12×C3⋊D4central extension (φ=1)48C6.119(S3xC2xC4)288,699

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