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Extensions 1→N→G→Q→1 with N=C20 and Q=C3⋊D4

Direct product G=N×Q with N=C20 and Q=C3⋊D4
dρLabelID
C20×C3⋊D4240C20xC3:D4480,807

Semidirect products G=N:Q with N=C20 and Q=C3⋊D4
extensionφ:Q→Aut NdρLabelID
C20⋊1(C3⋊D4) = C60⋊D4φ: C3⋊D4/C6 → C22 ⊆ Aut C20240C20:1(C3:D4)480,525
C20⋊2(C3⋊D4) = C12⋊7D20φ: C3⋊D4/C6 → C22 ⊆ Aut C20240C20:2(C3:D4)480,526
C20⋊3(C3⋊D4) = C60⋊10D4φ: C3⋊D4/C6 → C22 ⊆ Aut C20240C20:3(C3:D4)480,539
C20⋊4(C3⋊D4) = C12⋊2D20φ: C3⋊D4/C6 → C22 ⊆ Aut C20240C20:4(C3:D4)480,541
C20⋊5(C3⋊D4) = C60⋊2D4φ: C3⋊D4/C6 → C22 ⊆ Aut C20240C20:5(C3:D4)480,903
C20⋊6(C3⋊D4) = C60⋊3D4φ: C3⋊D4/C6 → C22 ⊆ Aut C20240C20:6(C3:D4)480,905
C20⋊7(C3⋊D4) = C12⋊D20φ: C3⋊D4/Dic3 → C2 ⊆ Aut C20240C20:7(C3:D4)480,534
C20⋊8(C3⋊D4) = C4×C3⋊D20φ: C3⋊D4/Dic3 → C2 ⊆ Aut C20240C20:8(C3:D4)480,519
C20⋊9(C3⋊D4) = C5×C12⋊3D4φ: C3⋊D4/Dic3 → C2 ⊆ Aut C20240C20:9(C3:D4)480,819
C20⋊10(C3⋊D4) = C60⋊4D4φ: C3⋊D4/D6 → C2 ⊆ Aut C20240C20:10(C3:D4)480,532
C20⋊11(C3⋊D4) = C4×C15⋊D4φ: C3⋊D4/D6 → C2 ⊆ Aut C20240C20:11(C3:D4)480,515
C20⋊12(C3⋊D4) = C5×D6⋊3D4φ: C3⋊D4/D6 → C2 ⊆ Aut C20240C20:12(C3:D4)480,817
C20⋊13(C3⋊D4) = C60⋊29D4φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C20240C20:13(C3:D4)480,895
C20⋊14(C3⋊D4) = C4×C15⋊7D4φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C20240C20:14(C3:D4)480,893
C20⋊15(C3⋊D4) = C5×C12⋊7D4φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C20240C20:15(C3:D4)480,809

Non-split extensions G=N.Q with N=C20 and Q=C3⋊D4
extensionφ:Q→Aut NdρLabelID
C20.1(C3⋊D4) = C15⋊D16φ: C3⋊D4/C6 → C22 ⊆ Aut C202404C20.1(C3:D4)480,13
C20.2(C3⋊D4) = C40.D6φ: C3⋊D4/C6 → C22 ⊆ Aut C202404C20.2(C3:D4)480,16
C20.3(C3⋊D4) = C15⋊SD32φ: C3⋊D4/C6 → C22 ⊆ Aut C202404C20.3(C3:D4)480,17
C20.4(C3⋊D4) = C15⋊Q32φ: C3⋊D4/C6 → C22 ⊆ Aut C204804C20.4(C3:D4)480,22
C20.5(C3⋊D4) = C20.5D12φ: C3⋊D4/C6 → C22 ⊆ Aut C201204C20.5(C3:D4)480,35
C20.6(C3⋊D4) = C60.29D4φ: C3⋊D4/C6 → C22 ⊆ Aut C201204+C20.6(C3:D4)480,36
C20.7(C3⋊D4) = C60.54D4φ: C3⋊D4/C6 → C22 ⊆ Aut C202404C20.7(C3:D4)480,38
C20.8(C3⋊D4) = C60.31D4φ: C3⋊D4/C6 → C22 ⊆ Aut C202404-C20.8(C3:D4)480,39
C20.9(C3⋊D4) = C30.D8φ: C3⋊D4/C6 → C22 ⊆ Aut C20240C20.9(C3:D4)480,40
C20.10(C3⋊D4) = C10.D24φ: C3⋊D4/C6 → C22 ⊆ Aut C20240C20.10(C3:D4)480,43
C20.11(C3⋊D4) = D60⋊15C4φ: C3⋊D4/C6 → C22 ⊆ Aut C20240C20.11(C3:D4)480,45
C20.12(C3⋊D4) = C30.Q16φ: C3⋊D4/C6 → C22 ⊆ Aut C20480C20.12(C3:D4)480,46
C20.13(C3⋊D4) = C10.Dic12φ: C3⋊D4/C6 → C22 ⊆ Aut C20480C20.13(C3:D4)480,49
C20.14(C3⋊D4) = Dic30⋊15C4φ: C3⋊D4/C6 → C22 ⊆ Aut C20480C20.14(C3:D4)480,51
C20.15(C3⋊D4) = C15⋊7D16φ: C3⋊D4/C6 → C22 ⊆ Aut C202404+C20.15(C3:D4)480,186
C20.16(C3⋊D4) = D8.D15φ: C3⋊D4/C6 → C22 ⊆ Aut C202404-C20.16(C3:D4)480,187
C20.17(C3⋊D4) = C8.6D30φ: C3⋊D4/C6 → C22 ⊆ Aut C202404+C20.17(C3:D4)480,188
C20.18(C3⋊D4) = C15⋊7Q32φ: C3⋊D4/C6 → C22 ⊆ Aut C204804-C20.18(C3:D4)480,189
C20.19(C3⋊D4) = D4⋊Dic15φ: C3⋊D4/C6 → C22 ⊆ Aut C20240C20.19(C3:D4)480,192
C20.20(C3⋊D4) = C60.8D4φ: C3⋊D4/C6 → C22 ⊆ Aut C201204C20.20(C3:D4)480,193
C20.21(C3⋊D4) = Q8⋊2Dic15φ: C3⋊D4/C6 → C22 ⊆ Aut C20480C20.21(C3:D4)480,195
C20.22(C3⋊D4) = C60.10D4φ: C3⋊D4/C6 → C22 ⊆ Aut C202404C20.22(C3:D4)480,196
C20.23(C3⋊D4) = C2×C15⋊D8φ: C3⋊D4/C6 → C22 ⊆ Aut C20240C20.23(C3:D4)480,372
C20.24(C3⋊D4) = D20⋊21D6φ: C3⋊D4/C6 → C22 ⊆ Aut C201204C20.24(C3:D4)480,375
C20.25(C3⋊D4) = D20⋊19D6φ: C3⋊D4/C6 → C22 ⊆ Aut C201204+C20.25(C3:D4)480,377
C20.26(C3⋊D4) = C2×C30.D4φ: C3⋊D4/C6 → C22 ⊆ Aut C20240C20.26(C3:D4)480,382
C20.27(C3⋊D4) = D20.37D6φ: C3⋊D4/C6 → C22 ⊆ Aut C202404C20.27(C3:D4)480,383
C20.28(C3⋊D4) = C2×C20.D6φ: C3⋊D4/C6 → C22 ⊆ Aut C20240C20.28(C3:D4)480,384
C20.29(C3⋊D4) = D60⋊30C22φ: C3⋊D4/C6 → C22 ⊆ Aut C201204C20.29(C3:D4)480,388
C20.30(C3⋊D4) = C60.63D4φ: C3⋊D4/C6 → C22 ⊆ Aut C202404-C20.30(C3:D4)480,389
C20.31(C3⋊D4) = C12.D20φ: C3⋊D4/C6 → C22 ⊆ Aut C202404C20.31(C3:D4)480,391
C20.32(C3⋊D4) = C2×C15⋊Q16φ: C3⋊D4/C6 → C22 ⊆ Aut C20480C20.32(C3:D4)480,394
C20.33(C3⋊D4) = C60.67D4φ: C3⋊D4/C6 → C22 ⊆ Aut C20240C20.33(C3:D4)480,435
C20.34(C3⋊D4) = C60.68D4φ: C3⋊D4/C6 → C22 ⊆ Aut C20240C20.34(C3:D4)480,436
C20.35(C3⋊D4) = C60.88D4φ: C3⋊D4/C6 → C22 ⊆ Aut C20240C20.35(C3:D4)480,444
C20.36(C3⋊D4) = C60.89D4φ: C3⋊D4/C6 → C22 ⊆ Aut C20240C20.36(C3:D4)480,446
C20.37(C3⋊D4) = Dic15⋊8Q8φ: C3⋊D4/C6 → C22 ⊆ Aut C20480C20.37(C3:D4)480,461
C20.38(C3⋊D4) = D30⋊10Q8φ: C3⋊D4/C6 → C22 ⊆ Aut C20240C20.38(C3:D4)480,466
C20.39(C3⋊D4) = C2×D4⋊D15φ: C3⋊D4/C6 → C22 ⊆ Aut C20240C20.39(C3:D4)480,896
C20.40(C3⋊D4) = D4.D30φ: C3⋊D4/C6 → C22 ⊆ Aut C201204C20.40(C3:D4)480,897
C20.41(C3⋊D4) = C2×D4.D15φ: C3⋊D4/C6 → C22 ⊆ Aut C20240C20.41(C3:D4)480,898
C20.42(C3⋊D4) = C60.17D4φ: C3⋊D4/C6 → C22 ⊆ Aut C20240C20.42(C3:D4)480,901
C20.43(C3⋊D4) = C2×Q8⋊2D15φ: C3⋊D4/C6 → C22 ⊆ Aut C20240C20.43(C3:D4)480,906
C20.44(C3⋊D4) = Q8.11D30φ: C3⋊D4/C6 → C22 ⊆ Aut C202404C20.44(C3:D4)480,907
C20.45(C3⋊D4) = C2×C15⋊7Q16φ: C3⋊D4/C6 → C22 ⊆ Aut C20480C20.45(C3:D4)480,908
C20.46(C3⋊D4) = Dic15⋊4Q8φ: C3⋊D4/C6 → C22 ⊆ Aut C20480C20.46(C3:D4)480,909
C20.47(C3⋊D4) = D30⋊7Q8φ: C3⋊D4/C6 → C22 ⊆ Aut C20240C20.47(C3:D4)480,911
C20.48(C3⋊D4) = C60.23D4φ: C3⋊D4/C6 → C22 ⊆ Aut C20240C20.48(C3:D4)480,912
C20.49(C3⋊D4) = C3⋊D80φ: C3⋊D4/Dic3 → C2 ⊆ Aut C202404+C20.49(C3:D4)480,14
C20.50(C3⋊D4) = D40.S3φ: C3⋊D4/Dic3 → C2 ⊆ Aut C202404-C20.50(C3:D4)480,18
C20.51(C3⋊D4) = C24.D10φ: C3⋊D4/Dic3 → C2 ⊆ Aut C202404+C20.51(C3:D4)480,19
C20.52(C3⋊D4) = C3⋊Dic40φ: C3⋊D4/Dic3 → C2 ⊆ Aut C204804-C20.52(C3:D4)480,23
C20.53(C3⋊D4) = C2×C3⋊D40φ: C3⋊D4/Dic3 → C2 ⊆ Aut C20240C20.53(C3:D4)480,376
C20.54(C3⋊D4) = C2×C6.D20φ: C3⋊D4/Dic3 → C2 ⊆ Aut C20240C20.54(C3:D4)480,386
C20.55(C3⋊D4) = C2×C15⋊SD16φ: C3⋊D4/Dic3 → C2 ⊆ Aut C20240C20.55(C3:D4)480,390
C20.56(C3⋊D4) = C2×C3⋊Dic20φ: C3⋊D4/Dic3 → C2 ⊆ Aut C20480C20.56(C3:D4)480,395
C20.57(C3⋊D4) = C60.44D4φ: C3⋊D4/Dic3 → C2 ⊆ Aut C20240C20.57(C3:D4)480,440
C20.58(C3⋊D4) = C60.47D4φ: C3⋊D4/Dic3 → C2 ⊆ Aut C20240C20.58(C3:D4)480,450
C20.59(C3⋊D4) = C60.48D4φ: C3⋊D4/Dic3 → C2 ⊆ Aut C20480C20.59(C3:D4)480,465
C20.60(C3⋊D4) = D30⋊4C8φ: C3⋊D4/Dic3 → C2 ⊆ Aut C20240C20.60(C3:D4)480,33
C20.61(C3⋊D4) = C60.97D4φ: C3⋊D4/Dic3 → C2 ⊆ Aut C201204C20.61(C3:D4)480,53
C20.62(C3⋊D4) = D60⋊13C4φ: C3⋊D4/Dic3 → C2 ⊆ Aut C201204C20.62(C3:D4)480,56
C20.63(C3⋊D4) = C60.15Q8φ: C3⋊D4/Dic3 → C2 ⊆ Aut C20480C20.63(C3:D4)480,60
C20.64(C3⋊D4) = C12.59D20φ: C3⋊D4/Dic3 → C2 ⊆ Aut C202404C20.64(C3:D4)480,69
C20.65(C3⋊D4) = D20.31D6φ: C3⋊D4/Dic3 → C2 ⊆ Aut C202404C20.65(C3:D4)480,387
C20.66(C3⋊D4) = C5×C3⋊D16φ: C3⋊D4/Dic3 → C2 ⊆ Aut C202404C20.66(C3:D4)480,145
C20.67(C3⋊D4) = C5×D8.S3φ: C3⋊D4/Dic3 → C2 ⊆ Aut C202404C20.67(C3:D4)480,146
C20.68(C3⋊D4) = C5×C8.6D6φ: C3⋊D4/Dic3 → C2 ⊆ Aut C202404C20.68(C3:D4)480,147
C20.69(C3⋊D4) = C5×C3⋊Q32φ: C3⋊D4/Dic3 → C2 ⊆ Aut C204804C20.69(C3:D4)480,148
C20.70(C3⋊D4) = C10×D4⋊S3φ: C3⋊D4/Dic3 → C2 ⊆ Aut C20240C20.70(C3:D4)480,810
C20.71(C3⋊D4) = C10×D4.S3φ: C3⋊D4/Dic3 → C2 ⊆ Aut C20240C20.71(C3:D4)480,812
C20.72(C3⋊D4) = C5×C23.12D6φ: C3⋊D4/Dic3 → C2 ⊆ Aut C20240C20.72(C3:D4)480,815
C20.73(C3⋊D4) = C10×Q8⋊2S3φ: C3⋊D4/Dic3 → C2 ⊆ Aut C20240C20.73(C3:D4)480,820
C20.74(C3⋊D4) = C10×C3⋊Q16φ: C3⋊D4/Dic3 → C2 ⊆ Aut C20480C20.74(C3:D4)480,822
C20.75(C3⋊D4) = C5×Dic3⋊Q8φ: C3⋊D4/Dic3 → C2 ⊆ Aut C20480C20.75(C3:D4)480,823
C20.76(C3⋊D4) = C5×C12.23D4φ: C3⋊D4/Dic3 → C2 ⊆ Aut C20240C20.76(C3:D4)480,826
C20.77(C3⋊D4) = C60.28D4φ: C3⋊D4/D6 → C2 ⊆ Aut C201204C20.77(C3:D4)480,34
C20.78(C3⋊D4) = C12.6D20φ: C3⋊D4/D6 → C2 ⊆ Aut C202404C20.78(C3:D4)480,37
C20.79(C3⋊D4) = C6.D40φ: C3⋊D4/D6 → C2 ⊆ Aut C20240C20.79(C3:D4)480,41
C20.80(C3⋊D4) = C6.Dic20φ: C3⋊D4/D6 → C2 ⊆ Aut C20480C20.80(C3:D4)480,47
C20.81(C3⋊D4) = C60.36D4φ: C3⋊D4/D6 → C2 ⊆ Aut C201204C20.81(C3:D4)480,374
C20.82(C3⋊D4) = D12.37D10φ: C3⋊D4/D6 → C2 ⊆ Aut C202404C20.82(C3:D4)480,385
C20.83(C3⋊D4) = C60.46D4φ: C3⋊D4/D6 → C2 ⊆ Aut C20240C20.83(C3:D4)480,445
C20.84(C3⋊D4) = C60.93D4φ: C3⋊D4/D6 → C2 ⊆ Aut C20240C20.84(C3:D4)480,31
C20.85(C3⋊D4) = C60.94D4φ: C3⋊D4/D6 → C2 ⊆ Aut C20240C20.85(C3:D4)480,32
C20.86(C3⋊D4) = C60.96D4φ: C3⋊D4/D6 → C2 ⊆ Aut C201204C20.86(C3:D4)480,52
C20.87(C3⋊D4) = C60.98D4φ: C3⋊D4/D6 → C2 ⊆ Aut C201204C20.87(C3:D4)480,54
C20.88(C3⋊D4) = C60.14Q8φ: C3⋊D4/D6 → C2 ⊆ Aut C20480C20.88(C3:D4)480,59
C20.89(C3⋊D4) = C60.D4φ: C3⋊D4/D6 → C2 ⊆ Aut C202404C20.89(C3:D4)480,68
C20.90(C3⋊D4) = D20.34D6φ: C3⋊D4/D6 → C2 ⊆ Aut C202404C20.90(C3:D4)480,373
C20.91(C3⋊D4) = C5×D4⋊Dic3φ: C3⋊D4/D6 → C2 ⊆ Aut C20240C20.91(C3:D4)480,151
C20.92(C3⋊D4) = C5×C12.D4φ: C3⋊D4/D6 → C2 ⊆ Aut C201204C20.92(C3:D4)480,152
C20.93(C3⋊D4) = C5×Q8⋊2Dic3φ: C3⋊D4/D6 → C2 ⊆ Aut C20480C20.93(C3:D4)480,154
C20.94(C3⋊D4) = C5×C12.10D4φ: C3⋊D4/D6 → C2 ⊆ Aut C202404C20.94(C3:D4)480,155
C20.95(C3⋊D4) = C5×D12⋊6C22φ: C3⋊D4/D6 → C2 ⊆ Aut C201204C20.95(C3:D4)480,811
C20.96(C3⋊D4) = C5×Q8.11D6φ: C3⋊D4/D6 → C2 ⊆ Aut C202404C20.96(C3:D4)480,821
C20.97(C3⋊D4) = C5×D6⋊3Q8φ: C3⋊D4/D6 → C2 ⊆ Aut C20240C20.97(C3:D4)480,825
C20.98(C3⋊D4) = Dic30⋊8C4φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C20480C20.98(C3:D4)480,176
C20.99(C3⋊D4) = D60⋊8C4φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C20240C20.99(C3:D4)480,181
C20.100(C3⋊D4) = M4(2)⋊D15φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C201204+C20.100(C3:D4)480,183
C20.101(C3⋊D4) = C4.D60φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C202404-C20.101(C3:D4)480,184
C20.102(C3⋊D4) = C60.205D4φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C20240C20.102(C3:D4)480,889
C20.103(C3⋊D4) = D4⋊D30φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C201204+C20.103(C3:D4)480,914
C20.104(C3⋊D4) = D4.9D30φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C202404-C20.104(C3:D4)480,916
C20.105(C3⋊D4) = C60.26Q8φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C20480C20.105(C3:D4)480,174
C20.106(C3⋊D4) = D30⋊3C8φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C20240C20.106(C3:D4)480,180
C20.107(C3⋊D4) = C60.210D4φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C202404C20.107(C3:D4)480,182
C20.108(C3⋊D4) = D60⋊10C4φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C201204C20.108(C3:D4)480,185
C20.109(C3⋊D4) = C60.212D4φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C20240C20.109(C3:D4)480,190
C20.110(C3⋊D4) = Q8⋊3Dic15φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C201204C20.110(C3:D4)480,197
C20.111(C3⋊D4) = D4.8D30φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C202404C20.111(C3:D4)480,915
C20.112(C3⋊D4) = C5×C2.Dic12φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C20480C20.112(C3:D4)480,135
C20.113(C3⋊D4) = C5×C2.D24φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C20240C20.113(C3:D4)480,140
C20.114(C3⋊D4) = C5×C12.46D4φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C201204C20.114(C3:D4)480,142
C20.115(C3⋊D4) = C5×C12.47D4φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C202404C20.115(C3:D4)480,143
C20.116(C3⋊D4) = C5×C12.48D4φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C20240C20.116(C3:D4)480,803
C20.117(C3⋊D4) = C5×D4⋊D6φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C201204C20.117(C3:D4)480,828
C20.118(C3⋊D4) = C5×Q8.14D6φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C202404C20.118(C3:D4)480,830
C20.119(C3⋊D4) = C5×Dic3⋊C8central extension (φ=1)480C20.119(C3:D4)480,133
C20.120(C3⋊D4) = C5×D6⋊C8central extension (φ=1)240C20.120(C3:D4)480,139
C20.121(C3⋊D4) = C5×C12.53D4central extension (φ=1)2404C20.121(C3:D4)480,141
C20.122(C3⋊D4) = C5×D12⋊C4central extension (φ=1)1204C20.122(C3:D4)480,144
C20.123(C3⋊D4) = C5×C12.55D4central extension (φ=1)240C20.123(C3:D4)480,149
C20.124(C3⋊D4) = C5×Q8⋊3Dic3central extension (φ=1)1204C20.124(C3:D4)480,156
C20.125(C3⋊D4) = C5×Q8.13D6central extension (φ=1)2404C20.125(C3:D4)480,829

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