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Extensions 1→N→G→Q→1 with N=C12 and Q=C5⋊D4

Direct product G=N×Q with N=C12 and Q=C5⋊D4
dρLabelID
C12×C5⋊D4240C12xC5:D4480,721

Semidirect products G=N:Q with N=C12 and Q=C5⋊D4
extensionφ:Q→Aut NdρLabelID
C12⋊1(C5⋊D4) = C60⋊4D4φ: C5⋊D4/C10 → C22 ⊆ Aut C12240C12:1(C5:D4)480,532
C12⋊2(C5⋊D4) = C60⋊6D4φ: C5⋊D4/C10 → C22 ⊆ Aut C12240C12:2(C5:D4)480,536
C12⋊3(C5⋊D4) = C60⋊10D4φ: C5⋊D4/C10 → C22 ⊆ Aut C12240C12:3(C5:D4)480,539
C12⋊4(C5⋊D4) = C20⋊2D12φ: C5⋊D4/C10 → C22 ⊆ Aut C12240C12:4(C5:D4)480,542
C12⋊5(C5⋊D4) = C60⋊2D4φ: C5⋊D4/C10 → C22 ⊆ Aut C12240C12:5(C5:D4)480,903
C12⋊6(C5⋊D4) = C60⋊3D4φ: C5⋊D4/C10 → C22 ⊆ Aut C12240C12:6(C5:D4)480,905
C12⋊7(C5⋊D4) = C20⋊D12φ: C5⋊D4/Dic5 → C2 ⊆ Aut C12240C12:7(C5:D4)480,527
C12⋊8(C5⋊D4) = C4×C5⋊D12φ: C5⋊D4/Dic5 → C2 ⊆ Aut C12240C12:8(C5:D4)480,521
C12⋊9(C5⋊D4) = C3×C20⋊D4φ: C5⋊D4/Dic5 → C2 ⊆ Aut C12240C12:9(C5:D4)480,733
C12⋊10(C5⋊D4) = C60⋊D4φ: C5⋊D4/D10 → C2 ⊆ Aut C12240C12:10(C5:D4)480,525
C12⋊11(C5⋊D4) = C4×C15⋊D4φ: C5⋊D4/D10 → C2 ⊆ Aut C12240C12:11(C5:D4)480,515
C12⋊12(C5⋊D4) = C3×C20⋊2D4φ: C5⋊D4/D10 → C2 ⊆ Aut C12240C12:12(C5:D4)480,731
C12⋊13(C5⋊D4) = C60⋊29D4φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C12240C12:13(C5:D4)480,895
C12⋊14(C5⋊D4) = C4×C15⋊7D4φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C12240C12:14(C5:D4)480,893
C12⋊15(C5⋊D4) = C3×C20⋊7D4φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C12240C12:15(C5:D4)480,723

Non-split extensions G=N.Q with N=C12 and Q=C5⋊D4
extensionφ:Q→Aut NdρLabelID
C12.1(C5⋊D4) = C15⋊D16φ: C5⋊D4/C10 → C22 ⊆ Aut C122404C12.1(C5:D4)480,13
C12.2(C5⋊D4) = C40.D6φ: C5⋊D4/C10 → C22 ⊆ Aut C122404C12.2(C5:D4)480,16
C12.3(C5⋊D4) = C15⋊SD32φ: C5⋊D4/C10 → C22 ⊆ Aut C122404C12.3(C5:D4)480,17
C12.4(C5⋊D4) = C15⋊Q32φ: C5⋊D4/C10 → C22 ⊆ Aut C124804C12.4(C5:D4)480,22
C12.5(C5⋊D4) = C60.28D4φ: C5⋊D4/C10 → C22 ⊆ Aut C121204C12.5(C5:D4)480,34
C12.6(C5⋊D4) = C20.5D12φ: C5⋊D4/C10 → C22 ⊆ Aut C121204C12.6(C5:D4)480,35
C12.7(C5⋊D4) = C60.29D4φ: C5⋊D4/C10 → C22 ⊆ Aut C121204+C12.7(C5:D4)480,36
C12.8(C5⋊D4) = C12.6D20φ: C5⋊D4/C10 → C22 ⊆ Aut C122404C12.8(C5:D4)480,37
C12.9(C5⋊D4) = C60.54D4φ: C5⋊D4/C10 → C22 ⊆ Aut C122404C12.9(C5:D4)480,38
C12.10(C5⋊D4) = C60.31D4φ: C5⋊D4/C10 → C22 ⊆ Aut C122404-C12.10(C5:D4)480,39
C12.11(C5⋊D4) = C6.D40φ: C5⋊D4/C10 → C22 ⊆ Aut C12240C12.11(C5:D4)480,41
C12.12(C5⋊D4) = D12⋊Dic5φ: C5⋊D4/C10 → C22 ⊆ Aut C12240C12.12(C5:D4)480,42
C12.13(C5⋊D4) = D60⋊12C4φ: C5⋊D4/C10 → C22 ⊆ Aut C12240C12.13(C5:D4)480,44
C12.14(C5⋊D4) = C6.Dic20φ: C5⋊D4/C10 → C22 ⊆ Aut C12480C12.14(C5:D4)480,47
C12.15(C5⋊D4) = Dic6⋊Dic5φ: C5⋊D4/C10 → C22 ⊆ Aut C12480C12.15(C5:D4)480,48
C12.16(C5⋊D4) = Dic30⋊12C4φ: C5⋊D4/C10 → C22 ⊆ Aut C12480C12.16(C5:D4)480,50
C12.17(C5⋊D4) = C15⋊7D16φ: C5⋊D4/C10 → C22 ⊆ Aut C122404+C12.17(C5:D4)480,186
C12.18(C5⋊D4) = D8.D15φ: C5⋊D4/C10 → C22 ⊆ Aut C122404-C12.18(C5:D4)480,187
C12.19(C5⋊D4) = C8.6D30φ: C5⋊D4/C10 → C22 ⊆ Aut C122404+C12.19(C5:D4)480,188
C12.20(C5⋊D4) = C15⋊7Q32φ: C5⋊D4/C10 → C22 ⊆ Aut C124804-C12.20(C5:D4)480,189
C12.21(C5⋊D4) = D4⋊Dic15φ: C5⋊D4/C10 → C22 ⊆ Aut C12240C12.21(C5:D4)480,192
C12.22(C5⋊D4) = C60.8D4φ: C5⋊D4/C10 → C22 ⊆ Aut C121204C12.22(C5:D4)480,193
C12.23(C5⋊D4) = Q8⋊2Dic15φ: C5⋊D4/C10 → C22 ⊆ Aut C12480C12.23(C5:D4)480,195
C12.24(C5⋊D4) = C60.10D4φ: C5⋊D4/C10 → C22 ⊆ Aut C122404C12.24(C5:D4)480,196
C12.25(C5⋊D4) = C2×C15⋊D8φ: C5⋊D4/C10 → C22 ⊆ Aut C12240C12.25(C5:D4)480,372
C12.26(C5⋊D4) = C60.36D4φ: C5⋊D4/C10 → C22 ⊆ Aut C121204C12.26(C5:D4)480,374
C12.27(C5⋊D4) = D60⋊36C22φ: C5⋊D4/C10 → C22 ⊆ Aut C121204C12.27(C5:D4)480,380
C12.28(C5⋊D4) = C60.38D4φ: C5⋊D4/C10 → C22 ⊆ Aut C121204+C12.28(C5:D4)480,381
C12.29(C5⋊D4) = C2×C30.D4φ: C5⋊D4/C10 → C22 ⊆ Aut C12240C12.29(C5:D4)480,382
C12.30(C5⋊D4) = C2×C20.D6φ: C5⋊D4/C10 → C22 ⊆ Aut C12240C12.30(C5:D4)480,384
C12.31(C5⋊D4) = D12.37D10φ: C5⋊D4/C10 → C22 ⊆ Aut C122404C12.31(C5:D4)480,385
C12.32(C5⋊D4) = C2×C15⋊Q16φ: C5⋊D4/C10 → C22 ⊆ Aut C12480C12.32(C5:D4)480,394
C12.33(C5⋊D4) = C20.D12φ: C5⋊D4/C10 → C22 ⊆ Aut C122404C12.33(C5:D4)480,397
C12.34(C5⋊D4) = D12.33D10φ: C5⋊D4/C10 → C22 ⊆ Aut C122404-C12.34(C5:D4)480,398
C12.35(C5⋊D4) = C60.45D4φ: C5⋊D4/C10 → C22 ⊆ Aut C12240C12.35(C5:D4)480,441
C12.36(C5⋊D4) = C60.88D4φ: C5⋊D4/C10 → C22 ⊆ Aut C12240C12.36(C5:D4)480,444
C12.37(C5⋊D4) = C60.46D4φ: C5⋊D4/C10 → C22 ⊆ Aut C12240C12.37(C5:D4)480,445
C12.38(C5⋊D4) = C60.89D4φ: C5⋊D4/C10 → C22 ⊆ Aut C12240C12.38(C5:D4)480,446
C12.39(C5⋊D4) = D30⋊9Q8φ: C5⋊D4/C10 → C22 ⊆ Aut C12240C12.39(C5:D4)480,459
C12.40(C5⋊D4) = Dic15⋊8Q8φ: C5⋊D4/C10 → C22 ⊆ Aut C12480C12.40(C5:D4)480,461
C12.41(C5⋊D4) = C2×D4⋊D15φ: C5⋊D4/C10 → C22 ⊆ Aut C12240C12.41(C5:D4)480,896
C12.42(C5⋊D4) = D4.D30φ: C5⋊D4/C10 → C22 ⊆ Aut C121204C12.42(C5:D4)480,897
C12.43(C5⋊D4) = C2×D4.D15φ: C5⋊D4/C10 → C22 ⊆ Aut C12240C12.43(C5:D4)480,898
C12.44(C5⋊D4) = C60.17D4φ: C5⋊D4/C10 → C22 ⊆ Aut C12240C12.44(C5:D4)480,901
C12.45(C5⋊D4) = C2×Q8⋊2D15φ: C5⋊D4/C10 → C22 ⊆ Aut C12240C12.45(C5:D4)480,906
C12.46(C5⋊D4) = Q8.11D30φ: C5⋊D4/C10 → C22 ⊆ Aut C122404C12.46(C5:D4)480,907
C12.47(C5⋊D4) = C2×C15⋊7Q16φ: C5⋊D4/C10 → C22 ⊆ Aut C12480C12.47(C5:D4)480,908
C12.48(C5⋊D4) = Dic15⋊4Q8φ: C5⋊D4/C10 → C22 ⊆ Aut C12480C12.48(C5:D4)480,909
C12.49(C5⋊D4) = D30⋊7Q8φ: C5⋊D4/C10 → C22 ⊆ Aut C12240C12.49(C5:D4)480,911
C12.50(C5⋊D4) = C60.23D4φ: C5⋊D4/C10 → C22 ⊆ Aut C12240C12.50(C5:D4)480,912
C12.51(C5⋊D4) = C5⋊D48φ: C5⋊D4/Dic5 → C2 ⊆ Aut C122404+C12.51(C5:D4)480,15
C12.52(C5⋊D4) = D24.D5φ: C5⋊D4/Dic5 → C2 ⊆ Aut C122404-C12.52(C5:D4)480,20
C12.53(C5⋊D4) = Dic12⋊D5φ: C5⋊D4/Dic5 → C2 ⊆ Aut C122404+C12.53(C5:D4)480,21
C12.54(C5⋊D4) = C5⋊Dic24φ: C5⋊D4/Dic5 → C2 ⊆ Aut C124804-C12.54(C5:D4)480,24
C12.55(C5⋊D4) = C2×C5⋊D24φ: C5⋊D4/Dic5 → C2 ⊆ Aut C12240C12.55(C5:D4)480,378
C12.56(C5⋊D4) = C2×D12.D5φ: C5⋊D4/Dic5 → C2 ⊆ Aut C12240C12.56(C5:D4)480,392
C12.57(C5⋊D4) = C2×Dic6⋊D5φ: C5⋊D4/Dic5 → C2 ⊆ Aut C12240C12.57(C5:D4)480,393
C12.58(C5⋊D4) = C2×C5⋊Dic12φ: C5⋊D4/Dic5 → C2 ⊆ Aut C12480C12.58(C5:D4)480,396
C12.59(C5⋊D4) = C60.69D4φ: C5⋊D4/Dic5 → C2 ⊆ Aut C12240C12.59(C5:D4)480,449
C12.60(C5⋊D4) = C60.70D4φ: C5⋊D4/Dic5 → C2 ⊆ Aut C12240C12.60(C5:D4)480,451
C12.61(C5⋊D4) = Dic5⋊Dic6φ: C5⋊D4/Dic5 → C2 ⊆ Aut C12480C12.61(C5:D4)480,452
C12.62(C5⋊D4) = C60.94D4φ: C5⋊D4/Dic5 → C2 ⊆ Aut C12240C12.62(C5:D4)480,32
C12.63(C5⋊D4) = D30⋊4C8φ: C5⋊D4/Dic5 → C2 ⊆ Aut C12240C12.63(C5:D4)480,33
C12.64(C5⋊D4) = C60.99D4φ: C5⋊D4/Dic5 → C2 ⊆ Aut C121204C12.64(C5:D4)480,55
C12.65(C5⋊D4) = D60⋊16C4φ: C5⋊D4/Dic5 → C2 ⊆ Aut C121204C12.65(C5:D4)480,57
C12.66(C5⋊D4) = C60.13Q8φ: C5⋊D4/Dic5 → C2 ⊆ Aut C12480C12.66(C5:D4)480,58
C12.67(C5⋊D4) = C60.105D4φ: C5⋊D4/Dic5 → C2 ⊆ Aut C122404C12.67(C5:D4)480,67
C12.68(C5⋊D4) = C20.60D12φ: C5⋊D4/Dic5 → C2 ⊆ Aut C122404C12.68(C5:D4)480,379
C12.69(C5⋊D4) = C3×C5⋊D16φ: C5⋊D4/Dic5 → C2 ⊆ Aut C122404C12.69(C5:D4)480,104
C12.70(C5⋊D4) = C3×D8.D5φ: C5⋊D4/Dic5 → C2 ⊆ Aut C122404C12.70(C5:D4)480,105
C12.71(C5⋊D4) = C3×C5⋊SD32φ: C5⋊D4/Dic5 → C2 ⊆ Aut C122404C12.71(C5:D4)480,106
C12.72(C5⋊D4) = C3×C5⋊Q32φ: C5⋊D4/Dic5 → C2 ⊆ Aut C124804C12.72(C5:D4)480,107
C12.73(C5⋊D4) = C6×D4⋊D5φ: C5⋊D4/Dic5 → C2 ⊆ Aut C12240C12.73(C5:D4)480,724
C12.74(C5⋊D4) = C6×D4.D5φ: C5⋊D4/Dic5 → C2 ⊆ Aut C12240C12.74(C5:D4)480,726
C12.75(C5⋊D4) = C3×C20.17D4φ: C5⋊D4/Dic5 → C2 ⊆ Aut C12240C12.75(C5:D4)480,729
C12.76(C5⋊D4) = C6×Q8⋊D5φ: C5⋊D4/Dic5 → C2 ⊆ Aut C12240C12.76(C5:D4)480,734
C12.77(C5⋊D4) = C6×C5⋊Q16φ: C5⋊D4/Dic5 → C2 ⊆ Aut C12480C12.77(C5:D4)480,736
C12.78(C5⋊D4) = C3×Dic5⋊Q8φ: C5⋊D4/Dic5 → C2 ⊆ Aut C12480C12.78(C5:D4)480,737
C12.79(C5⋊D4) = C3×C20.23D4φ: C5⋊D4/Dic5 → C2 ⊆ Aut C12240C12.79(C5:D4)480,740
C12.80(C5⋊D4) = C10.D24φ: C5⋊D4/D10 → C2 ⊆ Aut C12240C12.80(C5:D4)480,43
C12.81(C5⋊D4) = C10.Dic12φ: C5⋊D4/D10 → C2 ⊆ Aut C12480C12.81(C5:D4)480,49
C12.82(C5⋊D4) = D20⋊21D6φ: C5⋊D4/D10 → C2 ⊆ Aut C121204C12.82(C5:D4)480,375
C12.83(C5⋊D4) = D20.37D6φ: C5⋊D4/D10 → C2 ⊆ Aut C122404C12.83(C5:D4)480,383
C12.84(C5⋊D4) = C60.67D4φ: C5⋊D4/D10 → C2 ⊆ Aut C12240C12.84(C5:D4)480,435
C12.85(C5⋊D4) = C60.93D4φ: C5⋊D4/D10 → C2 ⊆ Aut C12240C12.85(C5:D4)480,31
C12.86(C5⋊D4) = C60.96D4φ: C5⋊D4/D10 → C2 ⊆ Aut C121204C12.86(C5:D4)480,52
C12.87(C5⋊D4) = C60.98D4φ: C5⋊D4/D10 → C2 ⊆ Aut C121204C12.87(C5:D4)480,54
C12.88(C5⋊D4) = C60.14Q8φ: C5⋊D4/D10 → C2 ⊆ Aut C12480C12.88(C5:D4)480,59
C12.89(C5⋊D4) = C60.D4φ: C5⋊D4/D10 → C2 ⊆ Aut C122404C12.89(C5:D4)480,68
C12.90(C5⋊D4) = D20.34D6φ: C5⋊D4/D10 → C2 ⊆ Aut C122404C12.90(C5:D4)480,373
C12.91(C5⋊D4) = C3×D4⋊Dic5φ: C5⋊D4/D10 → C2 ⊆ Aut C12240C12.91(C5:D4)480,110
C12.92(C5⋊D4) = C3×C20.D4φ: C5⋊D4/D10 → C2 ⊆ Aut C121204C12.92(C5:D4)480,111
C12.93(C5⋊D4) = C3×Q8⋊Dic5φ: C5⋊D4/D10 → C2 ⊆ Aut C12480C12.93(C5:D4)480,113
C12.94(C5⋊D4) = C3×C20.10D4φ: C5⋊D4/D10 → C2 ⊆ Aut C122404C12.94(C5:D4)480,114
C12.95(C5⋊D4) = C3×D4.D10φ: C5⋊D4/D10 → C2 ⊆ Aut C121204C12.95(C5:D4)480,725
C12.96(C5⋊D4) = C3×C20.C23φ: C5⋊D4/D10 → C2 ⊆ Aut C122404C12.96(C5:D4)480,735
C12.97(C5⋊D4) = C3×D10⋊3Q8φ: C5⋊D4/D10 → C2 ⊆ Aut C12240C12.97(C5:D4)480,739
C12.98(C5⋊D4) = Dic30⋊8C4φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C12480C12.98(C5:D4)480,176
C12.99(C5⋊D4) = D60⋊8C4φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C12240C12.99(C5:D4)480,181
C12.100(C5⋊D4) = M4(2)⋊D15φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C121204+C12.100(C5:D4)480,183
C12.101(C5⋊D4) = C4.D60φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C122404-C12.101(C5:D4)480,184
C12.102(C5⋊D4) = C60.205D4φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C12240C12.102(C5:D4)480,889
C12.103(C5⋊D4) = D4⋊D30φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C121204+C12.103(C5:D4)480,914
C12.104(C5⋊D4) = D4.9D30φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C122404-C12.104(C5:D4)480,916
C12.105(C5⋊D4) = C60.26Q8φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C12480C12.105(C5:D4)480,174
C12.106(C5⋊D4) = D30⋊3C8φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C12240C12.106(C5:D4)480,180
C12.107(C5⋊D4) = C60.210D4φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C122404C12.107(C5:D4)480,182
C12.108(C5⋊D4) = D60⋊10C4φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C121204C12.108(C5:D4)480,185
C12.109(C5⋊D4) = C60.212D4φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C12240C12.109(C5:D4)480,190
C12.110(C5⋊D4) = Q8⋊3Dic15φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C121204C12.110(C5:D4)480,197
C12.111(C5⋊D4) = D4.8D30φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C122404C12.111(C5:D4)480,915
C12.112(C5⋊D4) = C3×C20.44D4φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C12480C12.112(C5:D4)480,94
C12.113(C5⋊D4) = C3×D20⋊5C4φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C12240C12.113(C5:D4)480,99
C12.114(C5⋊D4) = C3×C20.46D4φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C121204C12.114(C5:D4)480,101
C12.115(C5⋊D4) = C3×C4.12D20φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C122404C12.115(C5:D4)480,102
C12.116(C5⋊D4) = C3×C20.48D4φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C12240C12.116(C5:D4)480,717
C12.117(C5⋊D4) = C3×D4⋊D10φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C121204C12.117(C5:D4)480,742
C12.118(C5⋊D4) = C3×D4.9D10φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C122404C12.118(C5:D4)480,744
C12.119(C5⋊D4) = C3×C20.8Q8central extension (φ=1)480C12.119(C5:D4)480,92
C12.120(C5⋊D4) = C3×D10⋊1C8central extension (φ=1)240C12.120(C5:D4)480,98
C12.121(C5⋊D4) = C3×C20.53D4central extension (φ=1)2404C12.121(C5:D4)480,100
C12.122(C5⋊D4) = C3×D20⋊7C4central extension (φ=1)1204C12.122(C5:D4)480,103
C12.123(C5⋊D4) = C3×C20.55D4central extension (φ=1)240C12.123(C5:D4)480,108
C12.124(C5⋊D4) = C3×D4⋊2Dic5central extension (φ=1)1204C12.124(C5:D4)480,115
C12.125(C5⋊D4) = C3×D4.8D10central extension (φ=1)2404C12.125(C5:D4)480,743

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