Extensions 1→N→G→Q→1 with N=C12 and Q=C4×S3

Direct product G=N×Q with N=C12 and Q=C4×S3
dρLabelID
S3×C4×C1296S3xC4xC12288,642

Semidirect products G=N:Q with N=C12 and Q=C4×S3
extensionφ:Q→Aut NdρLabelID
C121(C4×S3) = Dic3×D12φ: C4×S3/C6C22 ⊆ Aut C1296C12:1(C4xS3)288,540
C122(C4×S3) = D12⋊Dic3φ: C4×S3/C6C22 ⊆ Aut C1296C12:2(C4xS3)288,546
C123(C4×S3) = C62.70C23φ: C4×S3/C6C22 ⊆ Aut C1248C12:3(C4xS3)288,548
C124(C4×S3) = C4⋊C4×C3⋊S3φ: C4×S3/C6C22 ⊆ Aut C12144C12:4(C4xS3)288,748
C125(C4×S3) = C62.237C23φ: C4×S3/C6C22 ⊆ Aut C12144C12:5(C4xS3)288,750
C126(C4×S3) = Dic35D12φ: C4×S3/Dic3C2 ⊆ Aut C1248C12:6(C4xS3)288,542
C127(C4×S3) = C4×C6.D6φ: C4×S3/Dic3C2 ⊆ Aut C1248C12:7(C4xS3)288,530
C128(C4×S3) = C3×Dic35D4φ: C4×S3/Dic3C2 ⊆ Aut C1296C12:8(C4xS3)288,664
C129(C4×S3) = C4×C12⋊S3φ: C4×S3/C12C2 ⊆ Aut C12144C12:9(C4xS3)288,730
C1210(C4×S3) = C42×C3⋊S3φ: C4×S3/C12C2 ⊆ Aut C12144C12:10(C4xS3)288,728
C1211(C4×S3) = C12×D12φ: C4×S3/C12C2 ⊆ Aut C1296C12:11(C4xS3)288,644
C1212(C4×S3) = S3×C4⋊Dic3φ: C4×S3/D6C2 ⊆ Aut C1296C12:12(C4xS3)288,537
C1213(C4×S3) = C4×S3×Dic3φ: C4×S3/D6C2 ⊆ Aut C1296C12:13(C4xS3)288,523
C1214(C4×S3) = C3×S3×C4⋊C4φ: C4×S3/D6C2 ⊆ Aut C1296C12:14(C4xS3)288,662

Non-split extensions G=N.Q with N=C12 and Q=C4×S3
extensionφ:Q→Aut NdρLabelID
C12.1(C4×S3) = C36.Q8φ: C4×S3/C6C22 ⊆ Aut C12288C12.1(C4xS3)288,14
C12.2(C4×S3) = C4.Dic18φ: C4×S3/C6C22 ⊆ Aut C12288C12.2(C4xS3)288,15
C12.3(C4×S3) = C18.Q16φ: C4×S3/C6C22 ⊆ Aut C12288C12.3(C4xS3)288,16
C12.4(C4×S3) = C18.D8φ: C4×S3/C6C22 ⊆ Aut C12144C12.4(C4xS3)288,17
C12.5(C4×S3) = C36.53D4φ: C4×S3/C6C22 ⊆ Aut C121444C12.5(C4xS3)288,29
C12.6(C4×S3) = Dic18⋊C4φ: C4×S3/C6C22 ⊆ Aut C12724C12.6(C4xS3)288,32
C12.7(C4×S3) = Dic93Q8φ: C4×S3/C6C22 ⊆ Aut C12288C12.7(C4xS3)288,97
C12.8(C4×S3) = C4⋊C4×D9φ: C4×S3/C6C22 ⊆ Aut C12144C12.8(C4xS3)288,101
C12.9(C4×S3) = C4⋊C47D9φ: C4×S3/C6C22 ⊆ Aut C12144C12.9(C4xS3)288,102
C12.10(C4×S3) = D36⋊C4φ: C4×S3/C6C22 ⊆ Aut C12144C12.10(C4xS3)288,103
C12.11(C4×S3) = M4(2)×D9φ: C4×S3/C6C22 ⊆ Aut C12724C12.11(C4xS3)288,116
C12.12(C4×S3) = D36.C4φ: C4×S3/C6C22 ⊆ Aut C121444C12.12(C4xS3)288,117
C12.13(C4×S3) = D123Dic3φ: C4×S3/C6C22 ⊆ Aut C1296C12.13(C4xS3)288,210
C12.14(C4×S3) = C6.16D24φ: C4×S3/C6C22 ⊆ Aut C1296C12.14(C4xS3)288,211
C12.15(C4×S3) = C6.17D24φ: C4×S3/C6C22 ⊆ Aut C1248C12.15(C4xS3)288,212
C12.16(C4×S3) = Dic6⋊Dic3φ: C4×S3/C6C22 ⊆ Aut C1296C12.16(C4xS3)288,213
C12.17(C4×S3) = C6.Dic12φ: C4×S3/C6C22 ⊆ Aut C1296C12.17(C4xS3)288,214
C12.18(C4×S3) = D124Dic3φ: C4×S3/C6C22 ⊆ Aut C12244C12.18(C4xS3)288,216
C12.19(C4×S3) = D122Dic3φ: C4×S3/C6C22 ⊆ Aut C12484C12.19(C4xS3)288,217
C12.20(C4×S3) = C12.80D12φ: C4×S3/C6C22 ⊆ Aut C12484C12.20(C4xS3)288,218
C12.21(C4×S3) = C12.6Dic6φ: C4×S3/C6C22 ⊆ Aut C1296C12.21(C4xS3)288,222
C12.22(C4×S3) = C12.8Dic6φ: C4×S3/C6C22 ⊆ Aut C1296C12.22(C4xS3)288,224
C12.23(C4×S3) = C62.5Q8φ: C4×S3/C6C22 ⊆ Aut C12484C12.23(C4xS3)288,226
C12.24(C4×S3) = C12.9Dic6φ: C4×S3/C6C22 ⊆ Aut C12288C12.24(C4xS3)288,282
C12.25(C4×S3) = C12.10Dic6φ: C4×S3/C6C22 ⊆ Aut C12288C12.25(C4xS3)288,283
C12.26(C4×S3) = C62.113D4φ: C4×S3/C6C22 ⊆ Aut C12144C12.26(C4xS3)288,284
C12.27(C4×S3) = C62.114D4φ: C4×S3/C6C22 ⊆ Aut C12288C12.27(C4xS3)288,285
C12.28(C4×S3) = C62.8Q8φ: C4×S3/C6C22 ⊆ Aut C12144C12.28(C4xS3)288,297
C12.29(C4×S3) = C62.37D4φ: C4×S3/C6C22 ⊆ Aut C1272C12.29(C4xS3)288,300
C12.30(C4×S3) = D12.2Dic3φ: C4×S3/C6C22 ⊆ Aut C12484C12.30(C4xS3)288,462
C12.31(C4×S3) = D12.Dic3φ: C4×S3/C6C22 ⊆ Aut C12484C12.31(C4xS3)288,463
C12.32(C4×S3) = C3⋊C820D6φ: C4×S3/C6C22 ⊆ Aut C12244C12.32(C4xS3)288,466
C12.33(C4×S3) = Dic3×Dic6φ: C4×S3/C6C22 ⊆ Aut C1296C12.33(C4xS3)288,490
C12.34(C4×S3) = C62.13C23φ: C4×S3/C6C22 ⊆ Aut C1296C12.34(C4xS3)288,491
C12.35(C4×S3) = Dic36Dic6φ: C4×S3/C6C22 ⊆ Aut C1296C12.35(C4xS3)288,492
C12.36(C4×S3) = C62.19C23φ: C4×S3/C6C22 ⊆ Aut C1248C12.36(C4xS3)288,497
C12.37(C4×S3) = C62.231C23φ: C4×S3/C6C22 ⊆ Aut C12288C12.37(C4xS3)288,744
C12.38(C4×S3) = C62.236C23φ: C4×S3/C6C22 ⊆ Aut C12144C12.38(C4xS3)288,749
C12.39(C4×S3) = M4(2)×C3⋊S3φ: C4×S3/C6C22 ⊆ Aut C1272C12.39(C4xS3)288,763
C12.40(C4×S3) = C24.47D6φ: C4×S3/C6C22 ⊆ Aut C12144C12.40(C4xS3)288,764
C12.41(C4×S3) = C12.73D12φ: C4×S3/Dic3C2 ⊆ Aut C1296C12.41(C4xS3)288,215
C12.42(C4×S3) = C3⋊C8.22D6φ: C4×S3/Dic3C2 ⊆ Aut C12484C12.42(C4xS3)288,465
C12.43(C4×S3) = C24.60D6φ: C4×S3/Dic3C2 ⊆ Aut C12484C12.43(C4xS3)288,190
C12.44(C4×S3) = C24.62D6φ: C4×S3/Dic3C2 ⊆ Aut C12484C12.44(C4xS3)288,192
C12.45(C4×S3) = C3⋊C8⋊Dic3φ: C4×S3/Dic3C2 ⊆ Aut C1296C12.45(C4xS3)288,202
C12.46(C4×S3) = C2×C12.29D6φ: C4×S3/Dic3C2 ⊆ Aut C1248C12.46(C4xS3)288,464
C12.47(C4×S3) = C2×C12.31D6φ: C4×S3/Dic3C2 ⊆ Aut C1248C12.47(C4xS3)288,468
C12.48(C4×S3) = C62.44C23φ: C4×S3/Dic3C2 ⊆ Aut C1248C12.48(C4xS3)288,522
C12.49(C4×S3) = C3×C6.D8φ: C4×S3/Dic3C2 ⊆ Aut C1296C12.49(C4xS3)288,243
C12.50(C4×S3) = C3×C6.SD16φ: C4×S3/Dic3C2 ⊆ Aut C1296C12.50(C4xS3)288,244
C12.51(C4×S3) = C3×D12⋊C4φ: C4×S3/Dic3C2 ⊆ Aut C12484C12.51(C4xS3)288,259
C12.52(C4×S3) = C3×Dic6⋊C4φ: C4×S3/Dic3C2 ⊆ Aut C1296C12.52(C4xS3)288,658
C12.53(C4×S3) = C3×D12.C4φ: C4×S3/Dic3C2 ⊆ Aut C12484C12.53(C4xS3)288,678
C12.54(C4×S3) = C424D9φ: C4×S3/C12C2 ⊆ Aut C12722C12.54(C4xS3)288,12
C12.55(C4×S3) = C36.45D4φ: C4×S3/C12C2 ⊆ Aut C12288C12.55(C4xS3)288,24
C12.56(C4×S3) = C2.D72φ: C4×S3/C12C2 ⊆ Aut C12144C12.56(C4xS3)288,28
C12.57(C4×S3) = C4×Dic18φ: C4×S3/C12C2 ⊆ Aut C12288C12.57(C4xS3)288,78
C12.58(C4×S3) = C4×D36φ: C4×S3/C12C2 ⊆ Aut C12144C12.58(C4xS3)288,83
C12.59(C4×S3) = D36.2C4φ: C4×S3/C12C2 ⊆ Aut C121442C12.59(C4xS3)288,112
C12.60(C4×S3) = C122⋊C2φ: C4×S3/C12C2 ⊆ Aut C1272C12.60(C4xS3)288,280
C12.61(C4×S3) = C6.4Dic12φ: C4×S3/C12C2 ⊆ Aut C12288C12.61(C4xS3)288,291
C12.62(C4×S3) = C62.84D4φ: C4×S3/C12C2 ⊆ Aut C12144C12.62(C4xS3)288,296
C12.63(C4×S3) = C4×C324Q8φ: C4×S3/C12C2 ⊆ Aut C12288C12.63(C4xS3)288,725
C12.64(C4×S3) = C24.95D6φ: C4×S3/C12C2 ⊆ Aut C12144C12.64(C4xS3)288,758
C12.65(C4×S3) = C16×D9φ: C4×S3/C12C2 ⊆ Aut C121442C12.65(C4xS3)288,4
C12.66(C4×S3) = C16⋊D9φ: C4×S3/C12C2 ⊆ Aut C121442C12.66(C4xS3)288,5
C12.67(C4×S3) = C4×C9⋊C8φ: C4×S3/C12C2 ⊆ Aut C12288C12.67(C4xS3)288,9
C12.68(C4×S3) = C42.D9φ: C4×S3/C12C2 ⊆ Aut C12288C12.68(C4xS3)288,10
C12.69(C4×S3) = C8×Dic9φ: C4×S3/C12C2 ⊆ Aut C12288C12.69(C4xS3)288,21
C12.70(C4×S3) = C72⋊C4φ: C4×S3/C12C2 ⊆ Aut C12288C12.70(C4xS3)288,23
C12.71(C4×S3) = C42×D9φ: C4×S3/C12C2 ⊆ Aut C12144C12.71(C4xS3)288,81
C12.72(C4×S3) = C422D9φ: C4×S3/C12C2 ⊆ Aut C12144C12.72(C4xS3)288,82
C12.73(C4×S3) = C2×C8×D9φ: C4×S3/C12C2 ⊆ Aut C12144C12.73(C4xS3)288,110
C12.74(C4×S3) = C2×C8⋊D9φ: C4×S3/C12C2 ⊆ Aut C12144C12.74(C4xS3)288,111
C12.75(C4×S3) = C16×C3⋊S3φ: C4×S3/C12C2 ⊆ Aut C12144C12.75(C4xS3)288,272
C12.76(C4×S3) = C48⋊S3φ: C4×S3/C12C2 ⊆ Aut C12144C12.76(C4xS3)288,273
C12.77(C4×S3) = C4×C324C8φ: C4×S3/C12C2 ⊆ Aut C12288C12.77(C4xS3)288,277
C12.78(C4×S3) = C122.C2φ: C4×S3/C12C2 ⊆ Aut C12288C12.78(C4xS3)288,278
C12.79(C4×S3) = C8×C3⋊Dic3φ: C4×S3/C12C2 ⊆ Aut C12288C12.79(C4xS3)288,288
C12.80(C4×S3) = C24⋊Dic3φ: C4×S3/C12C2 ⊆ Aut C12288C12.80(C4xS3)288,290
C12.81(C4×S3) = C12216C2φ: C4×S3/C12C2 ⊆ Aut C12144C12.81(C4xS3)288,729
C12.82(C4×S3) = C2×C8×C3⋊S3φ: C4×S3/C12C2 ⊆ Aut C12144C12.82(C4xS3)288,756
C12.83(C4×S3) = C2×C24⋊S3φ: C4×S3/C12C2 ⊆ Aut C12144C12.83(C4xS3)288,757
C12.84(C4×S3) = C3×C424S3φ: C4×S3/C12C2 ⊆ Aut C12242C12.84(C4xS3)288,239
C12.85(C4×S3) = C3×C2.Dic12φ: C4×S3/C12C2 ⊆ Aut C1296C12.85(C4xS3)288,250
C12.86(C4×S3) = C3×C2.D24φ: C4×S3/C12C2 ⊆ Aut C1296C12.86(C4xS3)288,255
C12.87(C4×S3) = C12×Dic6φ: C4×S3/C12C2 ⊆ Aut C1296C12.87(C4xS3)288,639
C12.88(C4×S3) = C3×C8○D12φ: C4×S3/C12C2 ⊆ Aut C12482C12.88(C4xS3)288,672
C12.89(C4×S3) = C12.Dic6φ: C4×S3/D6C2 ⊆ Aut C1296C12.89(C4xS3)288,221
C12.90(C4×S3) = C6.18D24φ: C4×S3/D6C2 ⊆ Aut C1296C12.90(C4xS3)288,223
C12.91(C4×S3) = C12.82D12φ: C4×S3/D6C2 ⊆ Aut C12484C12.91(C4xS3)288,225
C12.92(C4×S3) = S3×C4.Dic3φ: C4×S3/D6C2 ⊆ Aut C12484C12.92(C4xS3)288,461
C12.93(C4×S3) = C62.11C23φ: C4×S3/D6C2 ⊆ Aut C1296C12.93(C4xS3)288,489
C12.94(C4×S3) = S3×C3⋊C16φ: C4×S3/D6C2 ⊆ Aut C12964C12.94(C4xS3)288,189
C12.95(C4×S3) = C24.61D6φ: C4×S3/D6C2 ⊆ Aut C12964C12.95(C4xS3)288,191
C12.96(C4×S3) = Dic3×C3⋊C8φ: C4×S3/D6C2 ⊆ Aut C1296C12.96(C4xS3)288,200
C12.97(C4×S3) = C6.(S3×C8)φ: C4×S3/D6C2 ⊆ Aut C1296C12.97(C4xS3)288,201
C12.98(C4×S3) = C2.Dic32φ: C4×S3/D6C2 ⊆ Aut C1296C12.98(C4xS3)288,203
C12.99(C4×S3) = C2×S3×C3⋊C8φ: C4×S3/D6C2 ⊆ Aut C1296C12.99(C4xS3)288,460
C12.100(C4×S3) = C2×D6.Dic3φ: C4×S3/D6C2 ⊆ Aut C1296C12.100(C4xS3)288,467
C12.101(C4×S3) = C62.25C23φ: C4×S3/D6C2 ⊆ Aut C1296C12.101(C4xS3)288,503
C12.102(C4×S3) = C3×C6.Q16φ: C4×S3/D6C2 ⊆ Aut C1296C12.102(C4xS3)288,241
C12.103(C4×S3) = C3×C12.Q8φ: C4×S3/D6C2 ⊆ Aut C1296C12.103(C4xS3)288,242
C12.104(C4×S3) = C3×C12.53D4φ: C4×S3/D6C2 ⊆ Aut C12484C12.104(C4xS3)288,256
C12.105(C4×S3) = C3×C4⋊C47S3φ: C4×S3/D6C2 ⊆ Aut C1296C12.105(C4xS3)288,663
C12.106(C4×S3) = C3×S3×M4(2)φ: C4×S3/D6C2 ⊆ Aut C12484C12.106(C4xS3)288,677
C12.107(C4×S3) = S3×C48central extension (φ=1)962C12.107(C4xS3)288,231
C12.108(C4×S3) = C3×D6.C8central extension (φ=1)962C12.108(C4xS3)288,232
C12.109(C4×S3) = C12×C3⋊C8central extension (φ=1)96C12.109(C4xS3)288,236
C12.110(C4×S3) = C3×C42.S3central extension (φ=1)96C12.110(C4xS3)288,237
C12.111(C4×S3) = Dic3×C24central extension (φ=1)96C12.111(C4xS3)288,247
C12.112(C4×S3) = C3×C24⋊C4central extension (φ=1)96C12.112(C4xS3)288,249
C12.113(C4×S3) = C3×C422S3central extension (φ=1)96C12.113(C4xS3)288,643
C12.114(C4×S3) = S3×C2×C24central extension (φ=1)96C12.114(C4xS3)288,670
C12.115(C4×S3) = C6×C8⋊S3central extension (φ=1)96C12.115(C4xS3)288,671

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