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Extensions 1→N→G→Q→1 with N=C4 and Q=C23⋊C4

Direct product G=N×Q with N=C4 and Q=C23⋊C4
dρLabelID
C4×C23⋊C432C4xC2^3:C4128,486

Semidirect products G=N:Q with N=C4 and Q=C23⋊C4
extensionφ:Q→Aut NdρLabelID
C4⋊1(C23⋊C4) = C24.175C23φ: C23⋊C4/C22⋊C4 → C2 ⊆ Aut C432C4:1(C2^3:C4)128,696
C4⋊2(C23⋊C4) = C24.167C23φ: C23⋊C4/C2×D4 → C2 ⊆ Aut C432C4:2(C2^3:C4)128,531

Non-split extensions G=N.Q with N=C4 and Q=C23⋊C4
extensionφ:Q→Aut NdρLabelID
C4.1(C23⋊C4) = C23.D8φ: C23⋊C4/C22⋊C4 → C2 ⊆ Aut C4168+C4.1(C2^3:C4)128,71
C4.2(C23⋊C4) = C23.2D8φ: C23⋊C4/C22⋊C4 → C2 ⊆ Aut C4328-C4.2(C2^3:C4)128,72
C4.3(C23⋊C4) = C23.SD16φ: C23⋊C4/C22⋊C4 → C2 ⊆ Aut C4168+C4.3(C2^3:C4)128,73
C4.4(C23⋊C4) = C23.2SD16φ: C23⋊C4/C22⋊C4 → C2 ⊆ Aut C4328-C4.4(C2^3:C4)128,74
C4.5(C23⋊C4) = C22.SD32φ: C23⋊C4/C22⋊C4 → C2 ⊆ Aut C432C4.5(C2^3:C4)128,79
C4.6(C23⋊C4) = C23.32D8φ: C23⋊C4/C22⋊C4 → C2 ⊆ Aut C432C4.6(C2^3:C4)128,80
C4.7(C23⋊C4) = C23.12SD16φ: C23⋊C4/C22⋊C4 → C2 ⊆ Aut C464C4.7(C2^3:C4)128,81
C4.8(C23⋊C4) = C23.13SD16φ: C23⋊C4/C22⋊C4 → C2 ⊆ Aut C464C4.8(C2^3:C4)128,82
C4.9(C23⋊C4) = C24.(C2×C4)φ: C23⋊C4/C22⋊C4 → C2 ⊆ Aut C432C4.9(C2^3:C4)128,203
C4.10(C23⋊C4) = C24.45(C2×C4)φ: C23⋊C4/C22⋊C4 → C2 ⊆ Aut C432C4.10(C2^3:C4)128,204
C4.11(C23⋊C4) = C24.54D4φ: C23⋊C4/C22⋊C4 → C2 ⊆ Aut C432C4.11(C2^3:C4)128,239
C4.12(C23⋊C4) = C24.55D4φ: C23⋊C4/C22⋊C4 → C2 ⊆ Aut C432C4.12(C2^3:C4)128,240
C4.13(C23⋊C4) = C24.60D4φ: C23⋊C4/C22⋊C4 → C2 ⊆ Aut C432C4.13(C2^3:C4)128,251
C4.14(C23⋊C4) = C24.61D4φ: C23⋊C4/C22⋊C4 → C2 ⊆ Aut C432C4.14(C2^3:C4)128,252
C4.15(C23⋊C4) = C24.176C23φ: C23⋊C4/C22⋊C4 → C2 ⊆ Aut C432C4.15(C2^3:C4)128,728
C4.16(C23⋊C4) = C2≀C4⋊C2φ: C23⋊C4/C22⋊C4 → C2 ⊆ Aut C4168+C4.16(C2^3:C4)128,854
C4.17(C23⋊C4) = C23.(C2×D4)φ: C23⋊C4/C22⋊C4 → C2 ⊆ Aut C4328-C4.17(C2^3:C4)128,855
C4.18(C23⋊C4) = C4.4D4⋊C4φ: C23⋊C4/C22⋊C4 → C2 ⊆ Aut C4168+C4.18(C2^3:C4)128,860
C4.19(C23⋊C4) = C4⋊Q8⋊C4φ: C23⋊C4/C22⋊C4 → C2 ⊆ Aut C4328-C4.19(C2^3:C4)128,861
C4.20(C23⋊C4) = C4⋊1D4.C4φ: C23⋊C4/C22⋊C4 → C2 ⊆ Aut C4168+C4.20(C2^3:C4)128,866
C4.21(C23⋊C4) = (C2×D4).137D4φ: C23⋊C4/C22⋊C4 → C2 ⊆ Aut C4328-C4.21(C2^3:C4)128,867
C4.22(C23⋊C4) = C23.8D8φ: C23⋊C4/C2×D4 → C2 ⊆ Aut C432C4.22(C2^3:C4)128,21
C4.23(C23⋊C4) = C24.2Q8φ: C23⋊C4/C2×D4 → C2 ⊆ Aut C432C4.23(C2^3:C4)128,25
C4.24(C23⋊C4) = C23.C42φ: C23⋊C4/C2×D4 → C2 ⊆ Aut C432C4.24(C2^3:C4)128,37
C4.25(C23⋊C4) = C23.2C42φ: C23⋊C4/C2×D4 → C2 ⊆ Aut C4324C4.25(C2^3:C4)128,123
C4.26(C23⋊C4) = C23.3C42φ: C23⋊C4/C2×D4 → C2 ⊆ Aut C4324C4.26(C2^3:C4)128,124
C4.27(C23⋊C4) = C23⋊M4(2)φ: C23⋊C4/C2×D4 → C2 ⊆ Aut C432C4.27(C2^3:C4)128,197
C4.28(C23⋊C4) = C24.58D4φ: C23⋊C4/C2×D4 → C2 ⊆ Aut C432C4.28(C2^3:C4)128,245
C4.29(C23⋊C4) = C4○C2≀C4φ: C23⋊C4/C2×D4 → C2 ⊆ Aut C4164C4.29(C2^3:C4)128,852
C4.30(C23⋊C4) = C4⋊Q8⋊29C4φ: C23⋊C4/C2×D4 → C2 ⊆ Aut C4164C4.30(C2^3:C4)128,858
C4.31(C23⋊C4) = (C2×D4).135D4φ: C23⋊C4/C2×D4 → C2 ⊆ Aut C4164C4.31(C2^3:C4)128,864
C4.32(C23⋊C4) = C23.21C42central extension (φ=1)32C4.32(C2^3:C4)128,14
C4.33(C23⋊C4) = C24.48D4central extension (φ=1)32C4.33(C2^3:C4)128,29
C4.34(C23⋊C4) = C24.3Q8central extension (φ=1)32C4.34(C2^3:C4)128,30
C4.35(C23⋊C4) = C23⋊C16central extension (φ=1)32C4.35(C2^3:C4)128,46
C4.36(C23⋊C4) = C23.M4(2)central extension (φ=1)64C4.36(C2^3:C4)128,47
C4.37(C23⋊C4) = C24.C8central extension (φ=1)164C4.37(C2^3:C4)128,52
C4.38(C23⋊C4) = C23.1M4(2)central extension (φ=1)324C4.38(C2^3:C4)128,53
C4.39(C23⋊C4) = C22.M5(2)central extension (φ=1)64C4.39(C2^3:C4)128,54
C4.40(C23⋊C4) = C23.7M4(2)central extension (φ=1)64C4.40(C2^3:C4)128,55
C4.41(C23⋊C4) = C42.C8central extension (φ=1)164C4.41(C2^3:C4)128,59
C4.42(C23⋊C4) = C22⋊C4.C8central extension (φ=1)324C4.42(C2^3:C4)128,60
C4.43(C23⋊C4) = (C22×C8)⋊C4central extension (φ=1)324C4.43(C2^3:C4)128,127
C4.44(C23⋊C4) = C23.8M4(2)central extension (φ=1)32C4.44(C2^3:C4)128,191
C4.45(C23⋊C4) = C24.53D4central extension (φ=1)32C4.45(C2^3:C4)128,233

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