# Extensions 1→N→G→Q→1 with N=C4 and Q=C2×C32⋊C4

Direct product G=N×Q with N=C4 and Q=C2×C32⋊C4
dρLabelID
C2×C4×C32⋊C448C2xC4xC3^2:C4288,932

Semidirect products G=N:Q with N=C4 and Q=C2×C32⋊C4
extensionφ:Q→Aut NdρLabelID
C41(C2×C32⋊C4) = D4×C32⋊C4φ: C2×C32⋊C4/C32⋊C4C2 ⊆ Aut C4248+C4:1(C2xC3^2:C4)288,936
C42(C2×C32⋊C4) = C2×C4⋊(C32⋊C4)φ: C2×C32⋊C4/C2×C3⋊S3C2 ⊆ Aut C448C4:2(C2xC3^2:C4)288,933

Non-split extensions G=N.Q with N=C4 and Q=C2×C32⋊C4
extensionφ:Q→Aut NdρLabelID
C4.1(C2×C32⋊C4) = C3⋊S3.5D8φ: C2×C32⋊C4/C32⋊C4C2 ⊆ Aut C4248+C4.1(C2xC3^2:C4)288,430
C4.2(C2×C32⋊C4) = C326C4≀C2φ: C2×C32⋊C4/C32⋊C4C2 ⊆ Aut C4488-C4.2(C2xC3^2:C4)288,431
C4.3(C2×C32⋊C4) = C3⋊S3.5Q16φ: C2×C32⋊C4/C32⋊C4C2 ⊆ Aut C4488-C4.3(C2xC3^2:C4)288,432
C4.4(C2×C32⋊C4) = C327C4≀C2φ: C2×C32⋊C4/C32⋊C4C2 ⊆ Aut C4488+C4.4(C2xC3^2:C4)288,433
C4.5(C2×C32⋊C4) = C62.(C2×C4)φ: C2×C32⋊C4/C32⋊C4C2 ⊆ Aut C4488-C4.5(C2xC3^2:C4)288,935
C4.6(C2×C32⋊C4) = C12⋊S3.C4φ: C2×C32⋊C4/C32⋊C4C2 ⊆ Aut C4488+C4.6(C2xC3^2:C4)288,937
C4.7(C2×C32⋊C4) = Q8×C32⋊C4φ: C2×C32⋊C4/C32⋊C4C2 ⊆ Aut C4488-C4.7(C2xC3^2:C4)288,938
C4.8(C2×C32⋊C4) = C8⋊(C32⋊C4)φ: C2×C32⋊C4/C2×C3⋊S3C2 ⊆ Aut C4484C4.8(C2xC3^2:C4)288,416
C4.9(C2×C32⋊C4) = C3⋊S3.4D8φ: C2×C32⋊C4/C2×C3⋊S3C2 ⊆ Aut C4484C4.9(C2xC3^2:C4)288,417
C4.10(C2×C32⋊C4) = (C3×C24).C4φ: C2×C32⋊C4/C2×C3⋊S3C2 ⊆ Aut C4484C4.10(C2xC3^2:C4)288,418
C4.11(C2×C32⋊C4) = C8.(C32⋊C4)φ: C2×C32⋊C4/C2×C3⋊S3C2 ⊆ Aut C4484C4.11(C2xC3^2:C4)288,419
C4.12(C2×C32⋊C4) = C2×C32⋊M4(2)φ: C2×C32⋊C4/C2×C3⋊S3C2 ⊆ Aut C448C4.12(C2xC3^2:C4)288,930
C4.13(C2×C32⋊C4) = C3⋊S3⋊M4(2)φ: C2×C32⋊C4/C2×C3⋊S3C2 ⊆ Aut C4244C4.13(C2xC3^2:C4)288,931
C4.14(C2×C32⋊C4) = (C6×C12)⋊5C4φ: C2×C32⋊C4/C2×C3⋊S3C2 ⊆ Aut C4244C4.14(C2xC3^2:C4)288,934
C4.15(C2×C32⋊C4) = C3⋊S33C16central extension (φ=1)484C4.15(C2xC3^2:C4)288,412
C4.16(C2×C32⋊C4) = C323M5(2)central extension (φ=1)484C4.16(C2xC3^2:C4)288,413
C4.17(C2×C32⋊C4) = C8×C32⋊C4central extension (φ=1)484C4.17(C2xC3^2:C4)288,414
C4.18(C2×C32⋊C4) = (C3×C24)⋊C4central extension (φ=1)484C4.18(C2xC3^2:C4)288,415
C4.19(C2×C32⋊C4) = C2×C322C16central extension (φ=1)96C4.19(C2xC3^2:C4)288,420
C4.20(C2×C32⋊C4) = C62.4C8central extension (φ=1)484C4.20(C2xC3^2:C4)288,421
C4.21(C2×C32⋊C4) = C2×C3⋊S33C8central extension (φ=1)48C4.21(C2xC3^2:C4)288,929

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