Extensions 1→N→G→Q→1 with N=C8 and Q=C32⋊C4

Direct product G=N×Q with N=C8 and Q=C32⋊C4

Semidirect products G=N:Q with N=C8 and Q=C32⋊C4
extensionφ:Q→Aut NdρLabelID
C81(C32⋊C4) = C3⋊S3.4D8φ: C32⋊C4/C3⋊S3C2 ⊆ Aut C8484C8:1(C3^2:C4)288,417
C82(C32⋊C4) = C8⋊(C32⋊C4)φ: C32⋊C4/C3⋊S3C2 ⊆ Aut C8484C8:2(C3^2:C4)288,416
C83(C32⋊C4) = (C3×C24)⋊C4φ: C32⋊C4/C3⋊S3C2 ⊆ Aut C8484C8:3(C3^2:C4)288,415

Non-split extensions G=N.Q with N=C8 and Q=C32⋊C4
extensionφ:Q→Aut NdρLabelID
C8.1(C32⋊C4) = C8.(C32⋊C4)φ: C32⋊C4/C3⋊S3C2 ⊆ Aut C8484C8.1(C3^2:C4)288,419
C8.2(C32⋊C4) = (C3×C24).C4φ: C32⋊C4/C3⋊S3C2 ⊆ Aut C8484C8.2(C3^2:C4)288,418
C8.3(C32⋊C4) = C323M5(2)φ: C32⋊C4/C3⋊S3C2 ⊆ Aut C8484C8.3(C3^2:C4)288,413
C8.4(C32⋊C4) = C322C32central extension (φ=1)964C8.4(C3^2:C4)288,188
C8.5(C32⋊C4) = C3⋊S33C16central extension (φ=1)484C8.5(C3^2:C4)288,412