# Extensions 1→N→G→Q→1 with N=C6 and Q=C2×S32

Direct product G=N×Q with N=C6 and Q=C2×S32
dρLabelID
S32×C2×C648S3^2xC2xC6432,767

Semidirect products G=N:Q with N=C6 and Q=C2×S32
extensionφ:Q→Aut NdρLabelID
C61(C2×S32) = C2×S33φ: C2×S32/S32C2 ⊆ Aut C6248+C6:1(C2xS3^2)432,759
C62(C2×S32) = C22×S3×C3⋊S3φ: C2×S32/S3×C6C2 ⊆ Aut C672C6:2(C2xS3^2)432,768
C63(C2×S32) = C22×C324D6φ: C2×S32/C2×C3⋊S3C2 ⊆ Aut C648C6:3(C2xS3^2)432,769

Non-split extensions G=N.Q with N=C6 and Q=C2×S32
extensionφ:Q→Aut NdρLabelID
C6.1(C2×S32) = S32×Dic3φ: C2×S32/S32C2 ⊆ Aut C6488-C6.1(C2xS3^2)432,594
C6.2(C2×S32) = S3×C6.D6φ: C2×S32/S32C2 ⊆ Aut C6248+C6.2(C2xS3^2)432,595
C6.3(C2×S32) = Dic36S32φ: C2×S32/S32C2 ⊆ Aut C6488-C6.3(C2xS3^2)432,596
C6.4(C2×S32) = S3×D6⋊S3φ: C2×S32/S32C2 ⊆ Aut C6488-C6.4(C2xS3^2)432,597
C6.5(C2×S32) = S3×C3⋊D12φ: C2×S32/S32C2 ⊆ Aut C6248+C6.5(C2xS3^2)432,598
C6.6(C2×S32) = D64S32φ: C2×S32/S32C2 ⊆ Aut C6248+C6.6(C2xS3^2)432,599
C6.7(C2×S32) = D6⋊S32φ: C2×S32/S32C2 ⊆ Aut C6488-C6.7(C2xS3^2)432,600
C6.8(C2×S32) = (S3×C6)⋊D6φ: C2×S32/S32C2 ⊆ Aut C6248+C6.8(C2xS3^2)432,601
C6.9(C2×S32) = C3⋊S34D12φ: C2×S32/S32C2 ⊆ Aut C6248+C6.9(C2xS3^2)432,602
C6.10(C2×S32) = S3×C322Q8φ: C2×S32/S32C2 ⊆ Aut C6488-C6.10(C2xS3^2)432,603
C6.11(C2×S32) = C335(C2×Q8)φ: C2×S32/S32C2 ⊆ Aut C6488-C6.11(C2xS3^2)432,604
C6.12(C2×S32) = C336(C2×Q8)φ: C2×S32/S32C2 ⊆ Aut C6248+C6.12(C2xS3^2)432,605
C6.13(C2×S32) = (S3×C6).D6φ: C2×S32/S32C2 ⊆ Aut C6248+C6.13(C2xS3^2)432,606
C6.14(C2×S32) = D6.S32φ: C2×S32/S32C2 ⊆ Aut C6488-C6.14(C2xS3^2)432,607
C6.15(C2×S32) = D6.4S32φ: C2×S32/S32C2 ⊆ Aut C6488-C6.15(C2xS3^2)432,608
C6.16(C2×S32) = D6.3S32φ: C2×S32/S32C2 ⊆ Aut C6248+C6.16(C2xS3^2)432,609
C6.17(C2×S32) = D6⋊S3⋊S3φ: C2×S32/S32C2 ⊆ Aut C6488-C6.17(C2xS3^2)432,610
C6.18(C2×S32) = D6.6S32φ: C2×S32/S32C2 ⊆ Aut C6488-C6.18(C2xS3^2)432,611
C6.19(C2×S32) = Dic3.S32φ: C2×S32/S32C2 ⊆ Aut C6248+C6.19(C2xS3^2)432,612
C6.20(C2×S32) = D9×Dic6φ: C2×S32/S3×C6C2 ⊆ Aut C61444-C6.20(C2xS3^2)432,280
C6.21(C2×S32) = D18.D6φ: C2×S32/S3×C6C2 ⊆ Aut C6724C6.21(C2xS3^2)432,281
C6.22(C2×S32) = Dic65D9φ: C2×S32/S3×C6C2 ⊆ Aut C6724+C6.22(C2xS3^2)432,282
C6.23(C2×S32) = Dic18⋊S3φ: C2×S32/S3×C6C2 ⊆ Aut C6724C6.23(C2xS3^2)432,283
C6.24(C2×S32) = S3×Dic18φ: C2×S32/S3×C6C2 ⊆ Aut C61444-C6.24(C2xS3^2)432,284
C6.25(C2×S32) = D125D9φ: C2×S32/S3×C6C2 ⊆ Aut C61444-C6.25(C2xS3^2)432,285
C6.26(C2×S32) = D12⋊D9φ: C2×S32/S3×C6C2 ⊆ Aut C6724C6.26(C2xS3^2)432,286
C6.27(C2×S32) = D6.D18φ: C2×S32/S3×C6C2 ⊆ Aut C6724C6.27(C2xS3^2)432,287
C6.28(C2×S32) = D365S3φ: C2×S32/S3×C6C2 ⊆ Aut C61444-C6.28(C2xS3^2)432,288
C6.29(C2×S32) = Dic9.D6φ: C2×S32/S3×C6C2 ⊆ Aut C6724+C6.29(C2xS3^2)432,289
C6.30(C2×S32) = C4×S3×D9φ: C2×S32/S3×C6C2 ⊆ Aut C6724C6.30(C2xS3^2)432,290
C6.31(C2×S32) = S3×D36φ: C2×S32/S3×C6C2 ⊆ Aut C6724+C6.31(C2xS3^2)432,291
C6.32(C2×S32) = D9×D12φ: C2×S32/S3×C6C2 ⊆ Aut C6724+C6.32(C2xS3^2)432,292
C6.33(C2×S32) = C36⋊D6φ: C2×S32/S3×C6C2 ⊆ Aut C6724C6.33(C2xS3^2)432,293
C6.34(C2×S32) = C2×C9⋊Dic6φ: C2×S32/S3×C6C2 ⊆ Aut C6144C6.34(C2xS3^2)432,303
C6.35(C2×S32) = C2×Dic3×D9φ: C2×S32/S3×C6C2 ⊆ Aut C6144C6.35(C2xS3^2)432,304
C6.36(C2×S32) = D18.3D6φ: C2×S32/S3×C6C2 ⊆ Aut C6724C6.36(C2xS3^2)432,305
C6.37(C2×S32) = C2×C18.D6φ: C2×S32/S3×C6C2 ⊆ Aut C672C6.37(C2xS3^2)432,306
C6.38(C2×S32) = C2×C3⋊D36φ: C2×S32/S3×C6C2 ⊆ Aut C672C6.38(C2xS3^2)432,307
C6.39(C2×S32) = C2×S3×Dic9φ: C2×S32/S3×C6C2 ⊆ Aut C6144C6.39(C2xS3^2)432,308
C6.40(C2×S32) = Dic3.D18φ: C2×S32/S3×C6C2 ⊆ Aut C6724C6.40(C2xS3^2)432,309
C6.41(C2×S32) = D18.4D6φ: C2×S32/S3×C6C2 ⊆ Aut C6724-C6.41(C2xS3^2)432,310
C6.42(C2×S32) = C2×D6⋊D9φ: C2×S32/S3×C6C2 ⊆ Aut C6144C6.42(C2xS3^2)432,311
C6.43(C2×S32) = C2×C9⋊D12φ: C2×S32/S3×C6C2 ⊆ Aut C672C6.43(C2xS3^2)432,312
C6.44(C2×S32) = S3×C9⋊D4φ: C2×S32/S3×C6C2 ⊆ Aut C6724C6.44(C2xS3^2)432,313
C6.45(C2×S32) = D9×C3⋊D4φ: C2×S32/S3×C6C2 ⊆ Aut C6724C6.45(C2xS3^2)432,314
C6.46(C2×S32) = D18⋊D6φ: C2×S32/S3×C6C2 ⊆ Aut C6364+C6.46(C2xS3^2)432,315
C6.47(C2×S32) = C22×S3×D9φ: C2×S32/S3×C6C2 ⊆ Aut C672C6.47(C2xS3^2)432,544
C6.48(C2×S32) = S3×C324Q8φ: C2×S32/S3×C6C2 ⊆ Aut C6144C6.48(C2xS3^2)432,660
C6.49(C2×S32) = (C3×D12)⋊S3φ: C2×S32/S3×C6C2 ⊆ Aut C6144C6.49(C2xS3^2)432,661
C6.50(C2×S32) = D12⋊(C3⋊S3)φ: C2×S32/S3×C6C2 ⊆ Aut C672C6.50(C2xS3^2)432,662
C6.51(C2×S32) = C3⋊S3×Dic6φ: C2×S32/S3×C6C2 ⊆ Aut C6144C6.51(C2xS3^2)432,663
C6.52(C2×S32) = C12.39S32φ: C2×S32/S3×C6C2 ⊆ Aut C672C6.52(C2xS3^2)432,664
C6.53(C2×S32) = C12.40S32φ: C2×S32/S3×C6C2 ⊆ Aut C672C6.53(C2xS3^2)432,665
C6.54(C2×S32) = C329(S3×Q8)φ: C2×S32/S3×C6C2 ⊆ Aut C672C6.54(C2xS3^2)432,666
C6.55(C2×S32) = C12.73S32φ: C2×S32/S3×C6C2 ⊆ Aut C672C6.55(C2xS3^2)432,667
C6.56(C2×S32) = C12.57S32φ: C2×S32/S3×C6C2 ⊆ Aut C6144C6.56(C2xS3^2)432,668
C6.57(C2×S32) = C12.58S32φ: C2×S32/S3×C6C2 ⊆ Aut C672C6.57(C2xS3^2)432,669
C6.58(C2×S32) = C4×S3×C3⋊S3φ: C2×S32/S3×C6C2 ⊆ Aut C672C6.58(C2xS3^2)432,670
C6.59(C2×S32) = S3×C12⋊S3φ: C2×S32/S3×C6C2 ⊆ Aut C672C6.59(C2xS3^2)432,671
C6.60(C2×S32) = C3⋊S3×D12φ: C2×S32/S3×C6C2 ⊆ Aut C672C6.60(C2xS3^2)432,672
C6.61(C2×S32) = C12⋊S32φ: C2×S32/S3×C6C2 ⊆ Aut C672C6.61(C2xS3^2)432,673
C6.62(C2×S32) = C2×S3×C3⋊Dic3φ: C2×S32/S3×C6C2 ⊆ Aut C6144C6.62(C2xS3^2)432,674
C6.63(C2×S32) = C62.90D6φ: C2×S32/S3×C6C2 ⊆ Aut C672C6.63(C2xS3^2)432,675
C6.64(C2×S32) = C62.91D6φ: C2×S32/S3×C6C2 ⊆ Aut C672C6.64(C2xS3^2)432,676
C6.65(C2×S32) = C2×Dic3×C3⋊S3φ: C2×S32/S3×C6C2 ⊆ Aut C6144C6.65(C2xS3^2)432,677
C6.66(C2×S32) = C62.93D6φ: C2×S32/S3×C6C2 ⊆ Aut C672C6.66(C2xS3^2)432,678
C6.67(C2×S32) = C2×C338(C2×C4)φ: C2×S32/S3×C6C2 ⊆ Aut C672C6.67(C2xS3^2)432,679
C6.68(C2×S32) = C2×C336D4φ: C2×S32/S3×C6C2 ⊆ Aut C6144C6.68(C2xS3^2)432,680
C6.69(C2×S32) = C2×C337D4φ: C2×S32/S3×C6C2 ⊆ Aut C672C6.69(C2xS3^2)432,681
C6.70(C2×S32) = C2×C338D4φ: C2×S32/S3×C6C2 ⊆ Aut C672C6.70(C2xS3^2)432,682
C6.71(C2×S32) = C2×C334Q8φ: C2×S32/S3×C6C2 ⊆ Aut C6144C6.71(C2xS3^2)432,683
C6.72(C2×S32) = S3×C327D4φ: C2×S32/S3×C6C2 ⊆ Aut C672C6.72(C2xS3^2)432,684
C6.73(C2×S32) = C3⋊S3×C3⋊D4φ: C2×S32/S3×C6C2 ⊆ Aut C672C6.73(C2xS3^2)432,685
C6.74(C2×S32) = C6223D6φ: C2×S32/S3×C6C2 ⊆ Aut C636C6.74(C2xS3^2)432,686
C6.75(C2×S32) = C3⋊S3⋊Dic6φ: C2×S32/C2×C3⋊S3C2 ⊆ Aut C67212-C6.75(C2xS3^2)432,294
C6.76(C2×S32) = C12⋊S3⋊S3φ: C2×S32/C2×C3⋊S3C2 ⊆ Aut C67212+C6.76(C2xS3^2)432,295
C6.77(C2×S32) = C12.84S32φ: C2×S32/C2×C3⋊S3C2 ⊆ Aut C6726C6.77(C2xS3^2)432,296
C6.78(C2×S32) = C12.91S32φ: C2×S32/C2×C3⋊S3C2 ⊆ Aut C6726C6.78(C2xS3^2)432,297
C6.79(C2×S32) = C12.85S32φ: C2×S32/C2×C3⋊S3C2 ⊆ Aut C6726-C6.79(C2xS3^2)432,298
C6.80(C2×S32) = C12.S32φ: C2×S32/C2×C3⋊S3C2 ⊆ Aut C67212-C6.80(C2xS3^2)432,299
C6.81(C2×S32) = C4×C32⋊D6φ: C2×S32/C2×C3⋊S3C2 ⊆ Aut C6366C6.81(C2xS3^2)432,300
C6.82(C2×S32) = C3⋊S3⋊D12φ: C2×S32/C2×C3⋊S3C2 ⊆ Aut C63612+C6.82(C2xS3^2)432,301
C6.83(C2×S32) = C12.86S32φ: C2×S32/C2×C3⋊S3C2 ⊆ Aut C6366+C6.83(C2xS3^2)432,302
C6.84(C2×S32) = C2×He32Q8φ: C2×S32/C2×C3⋊S3C2 ⊆ Aut C6144C6.84(C2xS3^2)432,316
C6.85(C2×S32) = C2×C6.S32φ: C2×S32/C2×C3⋊S3C2 ⊆ Aut C672C6.85(C2xS3^2)432,317
C6.86(C2×S32) = C62.8D6φ: C2×S32/C2×C3⋊S3C2 ⊆ Aut C67212-C6.86(C2xS3^2)432,318
C6.87(C2×S32) = C62.9D6φ: C2×S32/C2×C3⋊S3C2 ⊆ Aut C6726C6.87(C2xS3^2)432,319
C6.88(C2×S32) = C2×He32D4φ: C2×S32/C2×C3⋊S3C2 ⊆ Aut C672C6.88(C2xS3^2)432,320
C6.89(C2×S32) = C2×He3⋊(C2×C4)φ: C2×S32/C2×C3⋊S3C2 ⊆ Aut C672C6.89(C2xS3^2)432,321
C6.90(C2×S32) = C2×He33D4φ: C2×S32/C2×C3⋊S3C2 ⊆ Aut C672C6.90(C2xS3^2)432,322
C6.91(C2×S32) = C62⋊D6φ: C2×S32/C2×C3⋊S3C2 ⊆ Aut C63612+C6.91(C2xS3^2)432,323
C6.92(C2×S32) = C622D6φ: C2×S32/C2×C3⋊S3C2 ⊆ Aut C6366C6.92(C2xS3^2)432,324
C6.93(C2×S32) = C22×C32⋊D6φ: C2×S32/C2×C3⋊S3C2 ⊆ Aut C636C6.93(C2xS3^2)432,545
C6.94(C2×S32) = C3⋊S34Dic6φ: C2×S32/C2×C3⋊S3C2 ⊆ Aut C6484C6.94(C2xS3^2)432,687
C6.95(C2×S32) = C12⋊S312S3φ: C2×S32/C2×C3⋊S3C2 ⊆ Aut C6484C6.95(C2xS3^2)432,688
C6.96(C2×S32) = C12.95S32φ: C2×S32/C2×C3⋊S3C2 ⊆ Aut C6484C6.96(C2xS3^2)432,689
C6.97(C2×S32) = C4×C324D6φ: C2×S32/C2×C3⋊S3C2 ⊆ Aut C6484C6.97(C2xS3^2)432,690
C6.98(C2×S32) = C123S32φ: C2×S32/C2×C3⋊S3C2 ⊆ Aut C6484C6.98(C2xS3^2)432,691
C6.99(C2×S32) = C2×C339(C2×C4)φ: C2×S32/C2×C3⋊S3C2 ⊆ Aut C648C6.99(C2xS3^2)432,692
C6.100(C2×S32) = C62.96D6φ: C2×S32/C2×C3⋊S3C2 ⊆ Aut C6244C6.100(C2xS3^2)432,693
C6.101(C2×S32) = C2×C339D4φ: C2×S32/C2×C3⋊S3C2 ⊆ Aut C648C6.101(C2xS3^2)432,694
C6.102(C2×S32) = C2×C335Q8φ: C2×S32/C2×C3⋊S3C2 ⊆ Aut C648C6.102(C2xS3^2)432,695
C6.103(C2×S32) = C6224D6φ: C2×S32/C2×C3⋊S3C2 ⊆ Aut C6244C6.103(C2xS3^2)432,696
C6.104(C2×S32) = C3×S3×Dic6central extension (φ=1)484C6.104(C2xS3^2)432,642
C6.105(C2×S32) = C3×D125S3central extension (φ=1)484C6.105(C2xS3^2)432,643
C6.106(C2×S32) = C3×D12⋊S3central extension (φ=1)484C6.106(C2xS3^2)432,644
C6.107(C2×S32) = C3×Dic3.D6central extension (φ=1)484C6.107(C2xS3^2)432,645
C6.108(C2×S32) = C3×D6.D6central extension (φ=1)484C6.108(C2xS3^2)432,646
C6.109(C2×S32) = C3×D6.6D6central extension (φ=1)484C6.109(C2xS3^2)432,647
C6.110(C2×S32) = S32×C12central extension (φ=1)484C6.110(C2xS3^2)432,648
C6.111(C2×S32) = C3×S3×D12central extension (φ=1)484C6.111(C2xS3^2)432,649
C6.112(C2×S32) = C3×D6⋊D6central extension (φ=1)484C6.112(C2xS3^2)432,650
C6.113(C2×S32) = S3×C6×Dic3central extension (φ=1)48C6.113(C2xS3^2)432,651
C6.114(C2×S32) = C3×D6.3D6central extension (φ=1)244C6.114(C2xS3^2)432,652
C6.115(C2×S32) = C3×D6.4D6central extension (φ=1)244C6.115(C2xS3^2)432,653
C6.116(C2×S32) = C6×C6.D6central extension (φ=1)48C6.116(C2xS3^2)432,654
C6.117(C2×S32) = C6×D6⋊S3central extension (φ=1)48C6.117(C2xS3^2)432,655
C6.118(C2×S32) = C6×C3⋊D12central extension (φ=1)48C6.118(C2xS3^2)432,656
C6.119(C2×S32) = C6×C322Q8central extension (φ=1)48C6.119(C2xS3^2)432,657
C6.120(C2×S32) = C3×S3×C3⋊D4central extension (φ=1)244C6.120(C2xS3^2)432,658
C6.121(C2×S32) = C3×Dic3⋊D6central extension (φ=1)244C6.121(C2xS3^2)432,659

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