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

Direct product G=N×Q with N=C4 and Q=S3×C2×C4
dρLabelID
S3×C2×C4296S3xC2xC4^2192,1030

Semidirect products G=N:Q with N=C4 and Q=S3×C2×C4
extensionφ:Q→Aut NdρLabelID
C41(S3×C2×C4) = C4×S3×D4φ: S3×C2×C4/C4×S3C2 ⊆ Aut C448C4:1(S3xC2xC4)192,1103
C42(S3×C2×C4) = C2×Dic35D4φ: S3×C2×C4/C2×Dic3C2 ⊆ Aut C496C4:2(S3xC2xC4)192,1062
C43(S3×C2×C4) = C2×C4×D12φ: S3×C2×C4/C2×C12C2 ⊆ Aut C496C4:3(S3xC2xC4)192,1032
C44(S3×C2×C4) = C2×S3×C4⋊C4φ: S3×C2×C4/C22×S3C2 ⊆ Aut C496C4:4(S3xC2xC4)192,1060

Non-split extensions G=N.Q with N=C4 and Q=S3×C2×C4
extensionφ:Q→Aut NdρLabelID
C4.1(S3×C2×C4) = Dic34D8φ: S3×C2×C4/C4×S3C2 ⊆ Aut C496C4.1(S3xC2xC4)192,315
C4.2(S3×C2×C4) = D4.S3⋊C4φ: S3×C2×C4/C4×S3C2 ⊆ Aut C496C4.2(S3xC2xC4)192,316
C4.3(S3×C2×C4) = Dic36SD16φ: S3×C2×C4/C4×S3C2 ⊆ Aut C496C4.3(S3xC2xC4)192,317
C4.4(S3×C2×C4) = S3×D4⋊C4φ: S3×C2×C4/C4×S3C2 ⊆ Aut C448C4.4(S3xC2xC4)192,328
C4.5(S3×C2×C4) = C4⋊C419D6φ: S3×C2×C4/C4×S3C2 ⊆ Aut C448C4.5(S3xC2xC4)192,329
C4.6(S3×C2×C4) = D4⋊(C4×S3)φ: S3×C2×C4/C4×S3C2 ⊆ Aut C496C4.6(S3xC2xC4)192,330
C4.7(S3×C2×C4) = D42S3⋊C4φ: S3×C2×C4/C4×S3C2 ⊆ Aut C496C4.7(S3xC2xC4)192,331
C4.8(S3×C2×C4) = D4⋊S3⋊C4φ: S3×C2×C4/C4×S3C2 ⊆ Aut C496C4.8(S3xC2xC4)192,344
C4.9(S3×C2×C4) = Dic37SD16φ: S3×C2×C4/C4×S3C2 ⊆ Aut C496C4.9(S3xC2xC4)192,347
C4.10(S3×C2×C4) = C3⋊Q16⋊C4φ: S3×C2×C4/C4×S3C2 ⊆ Aut C4192C4.10(S3xC2xC4)192,348
C4.11(S3×C2×C4) = Dic34Q16φ: S3×C2×C4/C4×S3C2 ⊆ Aut C4192C4.11(S3xC2xC4)192,349
C4.12(S3×C2×C4) = S3×Q8⋊C4φ: S3×C2×C4/C4×S3C2 ⊆ Aut C496C4.12(S3xC2xC4)192,360
C4.13(S3×C2×C4) = (S3×Q8)⋊C4φ: S3×C2×C4/C4×S3C2 ⊆ Aut C496C4.13(S3xC2xC4)192,361
C4.14(S3×C2×C4) = Q87(C4×S3)φ: S3×C2×C4/C4×S3C2 ⊆ Aut C496C4.14(S3xC2xC4)192,362
C4.15(S3×C2×C4) = C4⋊C4.150D6φ: S3×C2×C4/C4×S3C2 ⊆ Aut C496C4.15(S3xC2xC4)192,363
C4.16(S3×C2×C4) = Q83(C4×S3)φ: S3×C2×C4/C4×S3C2 ⊆ Aut C496C4.16(S3xC2xC4)192,376
C4.17(S3×C2×C4) = S3×C4≀C2φ: S3×C2×C4/C4×S3C2 ⊆ Aut C4244C4.17(S3xC2xC4)192,379
C4.18(S3×C2×C4) = C423D6φ: S3×C2×C4/C4×S3C2 ⊆ Aut C4484C4.18(S3xC2xC4)192,380
C4.19(S3×C2×C4) = M4(2).22D6φ: S3×C2×C4/C4×S3C2 ⊆ Aut C4484C4.19(S3xC2xC4)192,382
C4.20(S3×C2×C4) = C42.196D6φ: S3×C2×C4/C4×S3C2 ⊆ Aut C4484C4.20(S3xC2xC4)192,383
C4.21(S3×C2×C4) = C4×D4⋊S3φ: S3×C2×C4/C4×S3C2 ⊆ Aut C496C4.21(S3xC2xC4)192,572
C4.22(S3×C2×C4) = C42.48D6φ: S3×C2×C4/C4×S3C2 ⊆ Aut C496C4.22(S3xC2xC4)192,573
C4.23(S3×C2×C4) = C4×D4.S3φ: S3×C2×C4/C4×S3C2 ⊆ Aut C496C4.23(S3xC2xC4)192,576
C4.24(S3×C2×C4) = C42.51D6φ: S3×C2×C4/C4×S3C2 ⊆ Aut C496C4.24(S3xC2xC4)192,577
C4.25(S3×C2×C4) = C4×Q82S3φ: S3×C2×C4/C4×S3C2 ⊆ Aut C496C4.25(S3xC2xC4)192,584
C4.26(S3×C2×C4) = C42.56D6φ: S3×C2×C4/C4×S3C2 ⊆ Aut C496C4.26(S3xC2xC4)192,585
C4.27(S3×C2×C4) = C4×C3⋊Q16φ: S3×C2×C4/C4×S3C2 ⊆ Aut C4192C4.27(S3xC2xC4)192,588
C4.28(S3×C2×C4) = C42.59D6φ: S3×C2×C4/C4×S3C2 ⊆ Aut C4192C4.28(S3xC2xC4)192,589
C4.29(S3×C2×C4) = C24.100D4φ: S3×C2×C4/C4×S3C2 ⊆ Aut C4484C4.29(S3xC2xC4)192,703
C4.30(S3×C2×C4) = C24.54D4φ: S3×C2×C4/C4×S3C2 ⊆ Aut C4484C4.30(S3xC2xC4)192,704
C4.31(S3×C2×C4) = C4×D42S3φ: S3×C2×C4/C4×S3C2 ⊆ Aut C496C4.31(S3xC2xC4)192,1095
C4.32(S3×C2×C4) = C4213D6φ: S3×C2×C4/C4×S3C2 ⊆ Aut C448C4.32(S3xC2xC4)192,1104
C4.33(S3×C2×C4) = C42.108D6φ: S3×C2×C4/C4×S3C2 ⊆ Aut C496C4.33(S3xC2xC4)192,1105
C4.34(S3×C2×C4) = C4×S3×Q8φ: S3×C2×C4/C4×S3C2 ⊆ Aut C496C4.34(S3xC2xC4)192,1130
C4.35(S3×C2×C4) = C42.125D6φ: S3×C2×C4/C4×S3C2 ⊆ Aut C496C4.35(S3xC2xC4)192,1131
C4.36(S3×C2×C4) = C4×Q83S3φ: S3×C2×C4/C4×S3C2 ⊆ Aut C496C4.36(S3xC2xC4)192,1132
C4.37(S3×C2×C4) = C42.126D6φ: S3×C2×C4/C4×S3C2 ⊆ Aut C496C4.37(S3xC2xC4)192,1133
C4.38(S3×C2×C4) = S3×C8○D4φ: S3×C2×C4/C4×S3C2 ⊆ Aut C4484C4.38(S3xC2xC4)192,1308
C4.39(S3×C2×C4) = M4(2)⋊28D6φ: S3×C2×C4/C4×S3C2 ⊆ Aut C4484C4.39(S3xC2xC4)192,1309
C4.40(S3×C2×C4) = Dic38SD16φ: S3×C2×C4/C2×Dic3C2 ⊆ Aut C496C4.40(S3xC2xC4)192,411
C4.41(S3×C2×C4) = Dic129C4φ: S3×C2×C4/C2×Dic3C2 ⊆ Aut C4192C4.41(S3xC2xC4)192,412
C4.42(S3×C2×C4) = D249C4φ: S3×C2×C4/C2×Dic3C2 ⊆ Aut C496C4.42(S3xC2xC4)192,428
C4.43(S3×C2×C4) = Dic35D8φ: S3×C2×C4/C2×Dic3C2 ⊆ Aut C496C4.43(S3xC2xC4)192,431
C4.44(S3×C2×C4) = Dic35Q16φ: S3×C2×C4/C2×Dic3C2 ⊆ Aut C4192C4.44(S3xC2xC4)192,432
C4.45(S3×C2×C4) = C24⋊C2⋊C4φ: S3×C2×C4/C2×Dic3C2 ⊆ Aut C496C4.45(S3xC2xC4)192,448
C4.46(S3×C2×C4) = D2410C4φ: S3×C2×C4/C2×Dic3C2 ⊆ Aut C4484C4.46(S3xC2xC4)192,453
C4.47(S3×C2×C4) = D247C4φ: S3×C2×C4/C2×Dic3C2 ⊆ Aut C4484C4.47(S3xC2xC4)192,454
C4.48(S3×C2×C4) = C2×C6.D8φ: S3×C2×C4/C2×Dic3C2 ⊆ Aut C496C4.48(S3xC2xC4)192,524
C4.49(S3×C2×C4) = C4○D12⋊C4φ: S3×C2×C4/C2×Dic3C2 ⊆ Aut C496C4.49(S3xC2xC4)192,525
C4.50(S3×C2×C4) = C2×C6.SD16φ: S3×C2×C4/C2×Dic3C2 ⊆ Aut C4192C4.50(S3xC2xC4)192,528
C4.51(S3×C2×C4) = C4⋊C436D6φ: S3×C2×C4/C2×Dic3C2 ⊆ Aut C448C4.51(S3xC2xC4)192,560
C4.52(S3×C2×C4) = C4.(C2×D12)φ: S3×C2×C4/C2×Dic3C2 ⊆ Aut C496C4.52(S3xC2xC4)192,561
C4.53(S3×C2×C4) = C4⋊C4.237D6φ: S3×C2×C4/C2×Dic3C2 ⊆ Aut C496C4.53(S3xC2xC4)192,563
C4.54(S3×C2×C4) = C2×D12⋊C4φ: S3×C2×C4/C2×Dic3C2 ⊆ Aut C448C4.54(S3xC2xC4)192,697
C4.55(S3×C2×C4) = M4(2)⋊24D6φ: S3×C2×C4/C2×Dic3C2 ⊆ Aut C4484C4.55(S3xC2xC4)192,698
C4.56(S3×C2×C4) = C2×Dic6⋊C4φ: S3×C2×C4/C2×Dic3C2 ⊆ Aut C4192C4.56(S3xC2xC4)192,1055
C4.57(S3×C2×C4) = C42.87D6φ: S3×C2×C4/C2×Dic3C2 ⊆ Aut C496C4.57(S3xC2xC4)192,1075
C4.58(S3×C2×C4) = C429D6φ: S3×C2×C4/C2×Dic3C2 ⊆ Aut C448C4.58(S3xC2xC4)192,1080
C4.59(S3×C2×C4) = C4×C24⋊C2φ: S3×C2×C4/C2×C12C2 ⊆ Aut C496C4.59(S3xC2xC4)192,250
C4.60(S3×C2×C4) = C4×D24φ: S3×C2×C4/C2×C12C2 ⊆ Aut C496C4.60(S3xC2xC4)192,251
C4.61(S3×C2×C4) = C4×Dic12φ: S3×C2×C4/C2×C12C2 ⊆ Aut C4192C4.61(S3xC2xC4)192,257
C4.62(S3×C2×C4) = D2411C4φ: S3×C2×C4/C2×C12C2 ⊆ Aut C4482C4.62(S3xC2xC4)192,259
C4.63(S3×C2×C4) = C42.16D6φ: S3×C2×C4/C2×C12C2 ⊆ Aut C496C4.63(S3xC2xC4)192,269
C4.64(S3×C2×C4) = D24⋊C4φ: S3×C2×C4/C2×C12C2 ⊆ Aut C496C4.64(S3xC2xC4)192,270
C4.65(S3×C2×C4) = Dic12⋊C4φ: S3×C2×C4/C2×C12C2 ⊆ Aut C4192C4.65(S3xC2xC4)192,275
C4.66(S3×C2×C4) = D244C4φ: S3×C2×C4/C2×C12C2 ⊆ Aut C4484C4.66(S3xC2xC4)192,276
C4.67(S3×C2×C4) = C2×C424S3φ: S3×C2×C4/C2×C12C2 ⊆ Aut C448C4.67(S3xC2xC4)192,486
C4.68(S3×C2×C4) = C426D6φ: S3×C2×C4/C2×C12C2 ⊆ Aut C4484C4.68(S3xC2xC4)192,564
C4.69(S3×C2×C4) = C2×C2.Dic12φ: S3×C2×C4/C2×C12C2 ⊆ Aut C4192C4.69(S3xC2xC4)192,662
C4.70(S3×C2×C4) = C2×C2.D24φ: S3×C2×C4/C2×C12C2 ⊆ Aut C496C4.70(S3xC2xC4)192,671
C4.71(S3×C2×C4) = C23.28D12φ: S3×C2×C4/C2×C12C2 ⊆ Aut C496C4.71(S3xC2xC4)192,672
C4.72(S3×C2×C4) = C23.51D12φ: S3×C2×C4/C2×C12C2 ⊆ Aut C496C4.72(S3xC2xC4)192,679
C4.73(S3×C2×C4) = C23.53D12φ: S3×C2×C4/C2×C12C2 ⊆ Aut C448C4.73(S3xC2xC4)192,690
C4.74(S3×C2×C4) = C23.54D12φ: S3×C2×C4/C2×C12C2 ⊆ Aut C496C4.74(S3xC2xC4)192,692
C4.75(S3×C2×C4) = C2×C4×Dic6φ: S3×C2×C4/C2×C12C2 ⊆ Aut C4192C4.75(S3xC2xC4)192,1026
C4.76(S3×C2×C4) = S3×C4.Q8φ: S3×C2×C4/C22×S3C2 ⊆ Aut C496C4.76(S3xC2xC4)192,418
C4.77(S3×C2×C4) = (S3×C8)⋊C4φ: S3×C2×C4/C22×S3C2 ⊆ Aut C496C4.77(S3xC2xC4)192,419
C4.78(S3×C2×C4) = C8⋊(C4×S3)φ: S3×C2×C4/C22×S3C2 ⊆ Aut C496C4.78(S3xC2xC4)192,420
C4.79(S3×C2×C4) = S3×C2.D8φ: S3×C2×C4/C22×S3C2 ⊆ Aut C496C4.79(S3xC2xC4)192,438
C4.80(S3×C2×C4) = C8.27(C4×S3)φ: S3×C2×C4/C22×S3C2 ⊆ Aut C496C4.80(S3xC2xC4)192,439
C4.81(S3×C2×C4) = C8⋊S3⋊C4φ: S3×C2×C4/C22×S3C2 ⊆ Aut C496C4.81(S3xC2xC4)192,440
C4.82(S3×C2×C4) = S3×C8.C4φ: S3×C2×C4/C22×S3C2 ⊆ Aut C4484C4.82(S3xC2xC4)192,451
C4.83(S3×C2×C4) = M4(2).25D6φ: S3×C2×C4/C22×S3C2 ⊆ Aut C4484C4.83(S3xC2xC4)192,452
C4.84(S3×C2×C4) = C2×C6.Q16φ: S3×C2×C4/C22×S3C2 ⊆ Aut C4192C4.84(S3xC2xC4)192,521
C4.85(S3×C2×C4) = C2×C12.Q8φ: S3×C2×C4/C22×S3C2 ⊆ Aut C4192C4.85(S3xC2xC4)192,522
C4.86(S3×C2×C4) = C4⋊C4.225D6φ: S3×C2×C4/C22×S3C2 ⊆ Aut C496C4.86(S3xC2xC4)192,523
C4.87(S3×C2×C4) = C4⋊C4.232D6φ: S3×C2×C4/C22×S3C2 ⊆ Aut C496C4.87(S3xC2xC4)192,554
C4.88(S3×C2×C4) = C4⋊C4.234D6φ: S3×C2×C4/C22×S3C2 ⊆ Aut C496C4.88(S3xC2xC4)192,557
C4.89(S3×C2×C4) = C2×C12.53D4φ: S3×C2×C4/C22×S3C2 ⊆ Aut C496C4.89(S3xC2xC4)192,682
C4.90(S3×C2×C4) = C23.8Dic6φ: S3×C2×C4/C22×S3C2 ⊆ Aut C4484C4.90(S3xC2xC4)192,683
C4.91(S3×C2×C4) = C2×C4⋊C47S3φ: S3×C2×C4/C22×S3C2 ⊆ Aut C496C4.91(S3xC2xC4)192,1061
C4.92(S3×C2×C4) = C6.82+ 1+4φ: S3×C2×C4/C22×S3C2 ⊆ Aut C496C4.92(S3xC2xC4)192,1063
C4.93(S3×C2×C4) = S3×C42⋊C2φ: S3×C2×C4/C22×S3C2 ⊆ Aut C448C4.93(S3xC2xC4)192,1079
C4.94(S3×C2×C4) = C42.91D6φ: S3×C2×C4/C22×S3C2 ⊆ Aut C496C4.94(S3xC2xC4)192,1082
C4.95(S3×C2×C4) = M4(2)⋊26D6φ: S3×C2×C4/C22×S3C2 ⊆ Aut C4484C4.95(S3xC2xC4)192,1304
C4.96(S3×C2×C4) = S3×C4×C8central extension (φ=1)96C4.96(S3xC2xC4)192,243
C4.97(S3×C2×C4) = C4×C8⋊S3central extension (φ=1)96C4.97(S3xC2xC4)192,246
C4.98(S3×C2×C4) = D6.C42central extension (φ=1)96C4.98(S3xC2xC4)192,248
C4.99(S3×C2×C4) = S3×C8⋊C4central extension (φ=1)96C4.99(S3xC2xC4)192,263
C4.100(S3×C2×C4) = Dic35M4(2)central extension (φ=1)96C4.100(S3xC2xC4)192,266
C4.101(S3×C2×C4) = D6.4C42central extension (φ=1)96C4.101(S3xC2xC4)192,267
C4.102(S3×C2×C4) = S3×C2×C16central extension (φ=1)96C4.102(S3xC2xC4)192,458
C4.103(S3×C2×C4) = C2×D6.C8central extension (φ=1)96C4.103(S3xC2xC4)192,459
C4.104(S3×C2×C4) = D12.4C8central extension (φ=1)962C4.104(S3xC2xC4)192,460
C4.105(S3×C2×C4) = S3×M5(2)central extension (φ=1)484C4.105(S3xC2xC4)192,465
C4.106(S3×C2×C4) = C16.12D6central extension (φ=1)964C4.106(S3xC2xC4)192,466
C4.107(S3×C2×C4) = C2×C4×C3⋊C8central extension (φ=1)192C4.107(S3xC2xC4)192,479
C4.108(S3×C2×C4) = C2×C42.S3central extension (φ=1)192C4.108(S3xC2xC4)192,480
C4.109(S3×C2×C4) = C4×C4.Dic3central extension (φ=1)96C4.109(S3xC2xC4)192,481
C4.110(S3×C2×C4) = C12.5C42central extension (φ=1)96C4.110(S3xC2xC4)192,556
C4.111(S3×C2×C4) = Dic3×C2×C8central extension (φ=1)192C4.111(S3xC2xC4)192,657
C4.112(S3×C2×C4) = C2×C24⋊C4central extension (φ=1)192C4.112(S3xC2xC4)192,659
C4.113(S3×C2×C4) = C12.12C42central extension (φ=1)96C4.113(S3xC2xC4)192,660
C4.114(S3×C2×C4) = Dic3×M4(2)central extension (φ=1)96C4.114(S3xC2xC4)192,676
C4.115(S3×C2×C4) = C12.7C42central extension (φ=1)96C4.115(S3xC2xC4)192,681
C4.116(S3×C2×C4) = C2×C422S3central extension (φ=1)96C4.116(S3xC2xC4)192,1031
C4.117(S3×C2×C4) = C4×C4○D12central extension (φ=1)96C4.117(S3xC2xC4)192,1033
C4.118(S3×C2×C4) = C42.188D6central extension (φ=1)96C4.118(S3xC2xC4)192,1081
C4.119(S3×C2×C4) = S3×C22×C8central extension (φ=1)96C4.119(S3xC2xC4)192,1295
C4.120(S3×C2×C4) = C22×C8⋊S3central extension (φ=1)96C4.120(S3xC2xC4)192,1296
C4.121(S3×C2×C4) = C2×C8○D12central extension (φ=1)96C4.121(S3xC2xC4)192,1297
C4.122(S3×C2×C4) = C2×S3×M4(2)central extension (φ=1)48C4.122(S3xC2xC4)192,1302
C4.123(S3×C2×C4) = C2×D12.C4central extension (φ=1)96C4.123(S3xC2xC4)192,1303

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