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Extensions 1→N→G→Q→1 with N=C2×C6 and Q=C5⋊D4

Direct product G=N×Q with N=C2×C6 and Q=C5⋊D4
dρLabelID
C2×C6×C5⋊D4240C2xC6xC5:D4480,1149

Semidirect products G=N:Q with N=C2×C6 and Q=C5⋊D4
extensionφ:Q→Aut NdρLabelID
(C2×C6)⋊1(C5⋊D4) = C15⋊C22≀C2φ: C5⋊D4/C10 → C22 ⊆ Aut C2×C6120(C2xC6):1(C5:D4)480,644
(C2×C6)⋊2(C5⋊D4) = (C2×C10)⋊11D12φ: C5⋊D4/C10 → C22 ⊆ Aut C2×C6120(C2xC6):2(C5:D4)480,646
(C2×C6)⋊3(C5⋊D4) = Dic15⋊18D4φ: C5⋊D4/C10 → C22 ⊆ Aut C2×C6240(C2xC6):3(C5:D4)480,647
(C2×C6)⋊4(C5⋊D4) = D30⋊19D4φ: C5⋊D4/C10 → C22 ⊆ Aut C2×C6120(C2xC6):4(C5:D4)480,649
(C2×C6)⋊5(C5⋊D4) = D30⋊17D4φ: C5⋊D4/C10 → C22 ⊆ Aut C2×C6120(C2xC6):5(C5:D4)480,902
(C2×C6)⋊6(C5⋊D4) = Dic15⋊12D4φ: C5⋊D4/C10 → C22 ⊆ Aut C2×C6240(C2xC6):6(C5:D4)480,904
(C2×C6)⋊7(C5⋊D4) = C3×Dic5⋊D4φ: C5⋊D4/Dic5 → C2 ⊆ Aut C2×C6240(C2xC6):7(C5:D4)480,732
(C2×C6)⋊8(C5⋊D4) = (C2×C10)⋊4D12φ: C5⋊D4/Dic5 → C2 ⊆ Aut C2×C6240(C2xC6):8(C5:D4)480,642
(C2×C6)⋊9(C5⋊D4) = C22×C5⋊D12φ: C5⋊D4/Dic5 → C2 ⊆ Aut C2×C6240(C2xC6):9(C5:D4)480,1120
(C2×C6)⋊10(C5⋊D4) = C3×C23⋊D10φ: C5⋊D4/D10 → C2 ⊆ Aut C2×C6120(C2xC6):10(C5:D4)480,730
(C2×C6)⋊11(C5⋊D4) = (C2×C30)⋊D4φ: C5⋊D4/D10 → C2 ⊆ Aut C2×C6120(C2xC6):11(C5:D4)480,639
(C2×C6)⋊12(C5⋊D4) = C22×C15⋊D4φ: C5⋊D4/D10 → C2 ⊆ Aut C2×C6240(C2xC6):12(C5:D4)480,1118
(C2×C6)⋊13(C5⋊D4) = C3×C24⋊2D5φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C2×C6120(C2xC6):13(C5:D4)480,746
(C2×C6)⋊14(C5⋊D4) = C24⋊5D15φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C2×C6120(C2xC6):14(C5:D4)480,918
(C2×C6)⋊15(C5⋊D4) = C22×C15⋊7D4φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C2×C6240(C2xC6):15(C5:D4)480,1179

Non-split extensions G=N.Q with N=C2×C6 and Q=C5⋊D4
extensionφ:Q→Aut NdρLabelID
(C2×C6).1(C5⋊D4) = C60.97D4φ: C5⋊D4/C10 → C22 ⊆ Aut C2×C61204(C2xC6).1(C5:D4)480,53
(C2×C6).2(C5⋊D4) = C60.98D4φ: C5⋊D4/C10 → C22 ⊆ Aut C2×C61204(C2xC6).2(C5:D4)480,54
(C2×C6).3(C5⋊D4) = D60⋊13C4φ: C5⋊D4/C10 → C22 ⊆ Aut C2×C61204(C2xC6).3(C5:D4)480,56
(C2×C6).4(C5⋊D4) = (C2×C6).D20φ: C5⋊D4/C10 → C22 ⊆ Aut C2×C61204(C2xC6).4(C5:D4)480,71
(C2×C6).5(C5⋊D4) = C15⋊8(C23⋊C4)φ: C5⋊D4/C10 → C22 ⊆ Aut C2×C61204(C2xC6).5(C5:D4)480,72
(C2×C6).6(C5⋊D4) = C15⋊9(C23⋊C4)φ: C5⋊D4/C10 → C22 ⊆ Aut C2×C61204(C2xC6).6(C5:D4)480,73
(C2×C6).7(C5⋊D4) = C23.7D30φ: C5⋊D4/C10 → C22 ⊆ Aut C2×C61204(C2xC6).7(C5:D4)480,194
(C2×C6).8(C5⋊D4) = Q8⋊3Dic15φ: C5⋊D4/C10 → C22 ⊆ Aut C2×C61204(C2xC6).8(C5:D4)480,197
(C2×C6).9(C5⋊D4) = D20.34D6φ: C5⋊D4/C10 → C22 ⊆ Aut C2×C62404(C2xC6).9(C5:D4)480,373
(C2×C6).10(C5⋊D4) = D20⋊21D6φ: C5⋊D4/C10 → C22 ⊆ Aut C2×C61204(C2xC6).10(C5:D4)480,375
(C2×C6).11(C5⋊D4) = D60⋊36C22φ: C5⋊D4/C10 → C22 ⊆ Aut C2×C61204(C2xC6).11(C5:D4)480,380
(C2×C6).12(C5⋊D4) = C60.38D4φ: C5⋊D4/C10 → C22 ⊆ Aut C2×C61204+(C2xC6).12(C5:D4)480,381
(C2×C6).13(C5⋊D4) = D20.37D6φ: C5⋊D4/C10 → C22 ⊆ Aut C2×C62404(C2xC6).13(C5:D4)480,383
(C2×C6).14(C5⋊D4) = C20.D12φ: C5⋊D4/C10 → C22 ⊆ Aut C2×C62404(C2xC6).14(C5:D4)480,397
(C2×C6).15(C5⋊D4) = D12.33D10φ: C5⋊D4/C10 → C22 ⊆ Aut C2×C62404-(C2xC6).15(C5:D4)480,398
(C2×C6).16(C5⋊D4) = (C2×C30).D4φ: C5⋊D4/C10 → C22 ⊆ Aut C2×C6240(C2xC6).16(C5:D4)480,612
(C2×C6).17(C5⋊D4) = C10.(C2×D12)φ: C5⋊D4/C10 → C22 ⊆ Aut C2×C6240(C2xC6).17(C5:D4)480,618
(C2×C6).18(C5⋊D4) = (C2×C10).D12φ: C5⋊D4/C10 → C22 ⊆ Aut C2×C6240(C2xC6).18(C5:D4)480,619
(C2×C6).19(C5⋊D4) = C23.22D30φ: C5⋊D4/C10 → C22 ⊆ Aut C2×C6240(C2xC6).19(C5:D4)480,900
(C2×C6).20(C5⋊D4) = D4⋊D30φ: C5⋊D4/C10 → C22 ⊆ Aut C2×C61204+(C2xC6).20(C5:D4)480,914
(C2×C6).21(C5⋊D4) = D4.8D30φ: C5⋊D4/C10 → C22 ⊆ Aut C2×C62404(C2xC6).21(C5:D4)480,915
(C2×C6).22(C5⋊D4) = D4.9D30φ: C5⋊D4/C10 → C22 ⊆ Aut C2×C62404-(C2xC6).22(C5:D4)480,916
(C2×C6).23(C5⋊D4) = C3×D4.8D10φ: C5⋊D4/Dic5 → C2 ⊆ Aut C2×C62404(C2xC6).23(C5:D4)480,743
(C2×C6).24(C5⋊D4) = C10.D24φ: C5⋊D4/Dic5 → C2 ⊆ Aut C2×C6240(C2xC6).24(C5:D4)480,43
(C2×C6).25(C5⋊D4) = D60⋊15C4φ: C5⋊D4/Dic5 → C2 ⊆ Aut C2×C6240(C2xC6).25(C5:D4)480,45
(C2×C6).26(C5⋊D4) = C10.Dic12φ: C5⋊D4/Dic5 → C2 ⊆ Aut C2×C6480(C2xC6).26(C5:D4)480,49
(C2×C6).27(C5⋊D4) = Dic30⋊15C4φ: C5⋊D4/Dic5 → C2 ⊆ Aut C2×C6480(C2xC6).27(C5:D4)480,51
(C2×C6).28(C5⋊D4) = C60.7Q8φ: C5⋊D4/Dic5 → C2 ⊆ Aut C2×C6480(C2xC6).28(C5:D4)480,61
(C2×C6).29(C5⋊D4) = C60.8Q8φ: C5⋊D4/Dic5 → C2 ⊆ Aut C2×C6480(C2xC6).29(C5:D4)480,64
(C2×C6).30(C5⋊D4) = C2×C5⋊D24φ: C5⋊D4/Dic5 → C2 ⊆ Aut C2×C6240(C2xC6).30(C5:D4)480,378
(C2×C6).31(C5⋊D4) = C20.60D12φ: C5⋊D4/Dic5 → C2 ⊆ Aut C2×C62404(C2xC6).31(C5:D4)480,379
(C2×C6).32(C5⋊D4) = C2×D12.D5φ: C5⋊D4/Dic5 → C2 ⊆ Aut C2×C6240(C2xC6).32(C5:D4)480,392
(C2×C6).33(C5⋊D4) = C2×Dic6⋊D5φ: C5⋊D4/Dic5 → C2 ⊆ Aut C2×C6240(C2xC6).33(C5:D4)480,393
(C2×C6).34(C5⋊D4) = C2×C5⋊Dic12φ: C5⋊D4/Dic5 → C2 ⊆ Aut C2×C6480(C2xC6).34(C5:D4)480,396
(C2×C6).35(C5⋊D4) = C2×D6⋊Dic5φ: C5⋊D4/Dic5 → C2 ⊆ Aut C2×C6240(C2xC6).35(C5:D4)480,614
(C2×C6).36(C5⋊D4) = C2×D30⋊4C4φ: C5⋊D4/Dic5 → C2 ⊆ Aut C2×C6240(C2xC6).36(C5:D4)480,616
(C2×C6).37(C5⋊D4) = C2×C30.Q8φ: C5⋊D4/Dic5 → C2 ⊆ Aut C2×C6480(C2xC6).37(C5:D4)480,617
(C2×C6).38(C5⋊D4) = C3×C23⋊Dic5φ: C5⋊D4/D10 → C2 ⊆ Aut C2×C61204(C2xC6).38(C5:D4)480,112
(C2×C6).39(C5⋊D4) = C3×D4⋊2Dic5φ: C5⋊D4/D10 → C2 ⊆ Aut C2×C61204(C2xC6).39(C5:D4)480,115
(C2×C6).40(C5⋊D4) = C3×C23.18D10φ: C5⋊D4/D10 → C2 ⊆ Aut C2×C6240(C2xC6).40(C5:D4)480,728
(C2×C6).41(C5⋊D4) = C3×D4⋊D10φ: C5⋊D4/D10 → C2 ⊆ Aut C2×C61204(C2xC6).41(C5:D4)480,742
(C2×C6).42(C5⋊D4) = C3×D4.9D10φ: C5⋊D4/D10 → C2 ⊆ Aut C2×C62404(C2xC6).42(C5:D4)480,744
(C2×C6).43(C5⋊D4) = C30.D8φ: C5⋊D4/D10 → C2 ⊆ Aut C2×C6240(C2xC6).43(C5:D4)480,40
(C2×C6).44(C5⋊D4) = D12⋊Dic5φ: C5⋊D4/D10 → C2 ⊆ Aut C2×C6240(C2xC6).44(C5:D4)480,42
(C2×C6).45(C5⋊D4) = C30.Q16φ: C5⋊D4/D10 → C2 ⊆ Aut C2×C6480(C2xC6).45(C5:D4)480,46
(C2×C6).46(C5⋊D4) = Dic6⋊Dic5φ: C5⋊D4/D10 → C2 ⊆ Aut C2×C6480(C2xC6).46(C5:D4)480,48
(C2×C6).47(C5⋊D4) = C60.99D4φ: C5⋊D4/D10 → C2 ⊆ Aut C2×C61204(C2xC6).47(C5:D4)480,55
(C2×C6).48(C5⋊D4) = C30.SD16φ: C5⋊D4/D10 → C2 ⊆ Aut C2×C6480(C2xC6).48(C5:D4)480,62
(C2×C6).49(C5⋊D4) = C30.20D8φ: C5⋊D4/D10 → C2 ⊆ Aut C2×C6480(C2xC6).49(C5:D4)480,65
(C2×C6).50(C5⋊D4) = C30.24C42φ: C5⋊D4/D10 → C2 ⊆ Aut C2×C6480(C2xC6).50(C5:D4)480,70
(C2×C6).51(C5⋊D4) = C2×C15⋊D8φ: C5⋊D4/D10 → C2 ⊆ Aut C2×C6240(C2xC6).51(C5:D4)480,372
(C2×C6).52(C5⋊D4) = C60.36D4φ: C5⋊D4/D10 → C2 ⊆ Aut C2×C61204(C2xC6).52(C5:D4)480,374
(C2×C6).53(C5⋊D4) = C2×C30.D4φ: C5⋊D4/D10 → C2 ⊆ Aut C2×C6240(C2xC6).53(C5:D4)480,382
(C2×C6).54(C5⋊D4) = C2×C20.D6φ: C5⋊D4/D10 → C2 ⊆ Aut C2×C6240(C2xC6).54(C5:D4)480,384
(C2×C6).55(C5⋊D4) = D12.37D10φ: C5⋊D4/D10 → C2 ⊆ Aut C2×C62404(C2xC6).55(C5:D4)480,385
(C2×C6).56(C5⋊D4) = C2×C15⋊Q16φ: C5⋊D4/D10 → C2 ⊆ Aut C2×C6480(C2xC6).56(C5:D4)480,394
(C2×C6).57(C5⋊D4) = C2×D10⋊Dic3φ: C5⋊D4/D10 → C2 ⊆ Aut C2×C6240(C2xC6).57(C5:D4)480,611
(C2×C6).58(C5⋊D4) = C30.(C2×D4)φ: C5⋊D4/D10 → C2 ⊆ Aut C2×C6240(C2xC6).58(C5:D4)480,615
(C2×C6).59(C5⋊D4) = C2×Dic15⋊5C4φ: C5⋊D4/D10 → C2 ⊆ Aut C2×C6480(C2xC6).59(C5:D4)480,620
(C2×C6).60(C5⋊D4) = C3×D20⋊4C4φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C2×C61202(C2xC6).60(C5:D4)480,83
(C2×C6).61(C5⋊D4) = C3×C23.1D10φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C2×C61204(C2xC6).61(C5:D4)480,84
(C2×C6).62(C5⋊D4) = C3×C23.23D10φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C2×C6240(C2xC6).62(C5:D4)480,722
(C2×C6).63(C5⋊D4) = C3×D4.D10φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C2×C61204(C2xC6).63(C5:D4)480,725
(C2×C6).64(C5⋊D4) = C3×C20.C23φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C2×C62404(C2xC6).64(C5:D4)480,735
(C2×C6).65(C5⋊D4) = D60⋊7C4φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C2×C61202(C2xC6).65(C5:D4)480,165
(C2×C6).66(C5⋊D4) = C23.6D30φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C2×C61204(C2xC6).66(C5:D4)480,166
(C2×C6).67(C5⋊D4) = C60.1Q8φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C2×C6480(C2xC6).67(C5:D4)480,167
(C2×C6).68(C5⋊D4) = C60.2Q8φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C2×C6480(C2xC6).68(C5:D4)480,168
(C2×C6).69(C5⋊D4) = D60⋊9C4φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C2×C6240(C2xC6).69(C5:D4)480,169
(C2×C6).70(C5⋊D4) = Dic30⋊9C4φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C2×C6480(C2xC6).70(C5:D4)480,170
(C2×C6).71(C5⋊D4) = C30.29C42φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C2×C6480(C2xC6).71(C5:D4)480,191
(C2×C6).72(C5⋊D4) = D4⋊Dic15φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C2×C6240(C2xC6).72(C5:D4)480,192
(C2×C6).73(C5⋊D4) = Q8⋊2Dic15φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C2×C6480(C2xC6).73(C5:D4)480,195
(C2×C6).74(C5⋊D4) = C2×C30.4Q8φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C2×C6480(C2xC6).74(C5:D4)480,888
(C2×C6).75(C5⋊D4) = C2×D30⋊3C4φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C2×C6240(C2xC6).75(C5:D4)480,892
(C2×C6).76(C5⋊D4) = C23.28D30φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C2×C6240(C2xC6).76(C5:D4)480,894
(C2×C6).77(C5⋊D4) = C2×D4⋊D15φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C2×C6240(C2xC6).77(C5:D4)480,896
(C2×C6).78(C5⋊D4) = D4.D30φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C2×C61204(C2xC6).78(C5:D4)480,897
(C2×C6).79(C5⋊D4) = C2×D4.D15φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C2×C6240(C2xC6).79(C5:D4)480,898
(C2×C6).80(C5⋊D4) = C2×Q8⋊2D15φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C2×C6240(C2xC6).80(C5:D4)480,906
(C2×C6).81(C5⋊D4) = Q8.11D30φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C2×C62404(C2xC6).81(C5:D4)480,907
(C2×C6).82(C5⋊D4) = C2×C15⋊7Q16φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C2×C6480(C2xC6).82(C5:D4)480,908
(C2×C6).83(C5⋊D4) = C2×C30.38D4φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C2×C6240(C2xC6).83(C5:D4)480,917
(C2×C6).84(C5⋊D4) = C3×C10.D8central extension (φ=1)480(C2xC6).84(C5:D4)480,85
(C2×C6).85(C5⋊D4) = C3×C20.Q8central extension (φ=1)480(C2xC6).85(C5:D4)480,86
(C2×C6).86(C5⋊D4) = C3×D20⋊6C4central extension (φ=1)240(C2xC6).86(C5:D4)480,87
(C2×C6).87(C5⋊D4) = C3×C10.Q16central extension (φ=1)480(C2xC6).87(C5:D4)480,88
(C2×C6).88(C5⋊D4) = C3×C10.10C42central extension (φ=1)480(C2xC6).88(C5:D4)480,109
(C2×C6).89(C5⋊D4) = C3×D4⋊Dic5central extension (φ=1)240(C2xC6).89(C5:D4)480,110
(C2×C6).90(C5⋊D4) = C3×Q8⋊Dic5central extension (φ=1)480(C2xC6).90(C5:D4)480,113
(C2×C6).91(C5⋊D4) = C6×C10.D4central extension (φ=1)480(C2xC6).91(C5:D4)480,716
(C2×C6).92(C5⋊D4) = C6×D10⋊C4central extension (φ=1)240(C2xC6).92(C5:D4)480,720
(C2×C6).93(C5⋊D4) = C6×D4⋊D5central extension (φ=1)240(C2xC6).93(C5:D4)480,724
(C2×C6).94(C5⋊D4) = C6×D4.D5central extension (φ=1)240(C2xC6).94(C5:D4)480,726
(C2×C6).95(C5⋊D4) = C6×Q8⋊D5central extension (φ=1)240(C2xC6).95(C5:D4)480,734
(C2×C6).96(C5⋊D4) = C6×C5⋊Q16central extension (φ=1)480(C2xC6).96(C5:D4)480,736
(C2×C6).97(C5⋊D4) = C6×C23.D5central extension (φ=1)240(C2xC6).97(C5:D4)480,745

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