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

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

Semidirect products G=N:Q with N=C2×C4 and Q=C32⋊C4
extensionφ:Q→Aut NdρLabelID
(C2×C4)⋊(C32⋊C4) = (C6×C12)⋊C4φ: C32⋊C4/C32C4 ⊆ Aut C2×C4244+(C2xC4):(C3^2:C4)288,422
(C2×C4)⋊2(C32⋊C4) = (C6×C12)⋊2C4φ: C32⋊C4/C3⋊S3C2 ⊆ Aut C2×C448(C2xC4):2(C3^2:C4)288,429
(C2×C4)⋊3(C32⋊C4) = C2×C4⋊(C32⋊C4)φ: C32⋊C4/C3⋊S3C2 ⊆ Aut C2×C448(C2xC4):3(C3^2:C4)288,933
(C2×C4)⋊4(C32⋊C4) = (C6×C12)⋊5C4φ: C32⋊C4/C3⋊S3C2 ⊆ Aut C2×C4244(C2xC4):4(C3^2:C4)288,934

Non-split extensions G=N.Q with N=C2×C4 and Q=C32⋊C4
extensionφ:Q→Aut NdρLabelID
(C2×C4).(C32⋊C4) = C3⋊Dic3.D4φ: C32⋊C4/C32C4 ⊆ Aut C2×C4484-(C2xC4).(C3^2:C4)288,428
(C2×C4).2(C32⋊C4) = C322C8⋊C4φ: C32⋊C4/C3⋊S3C2 ⊆ Aut C2×C496(C2xC4).2(C3^2:C4)288,425
(C2×C4).3(C32⋊C4) = C62.6(C2×C4)φ: C32⋊C4/C3⋊S3C2 ⊆ Aut C2×C448(C2xC4).3(C3^2:C4)288,426
(C2×C4).4(C32⋊C4) = C325(C4⋊C8)φ: C32⋊C4/C3⋊S3C2 ⊆ Aut C2×C496(C2xC4).4(C3^2:C4)288,427
(C2×C4).5(C32⋊C4) = C62.4C8φ: C32⋊C4/C3⋊S3C2 ⊆ Aut C2×C4484(C2xC4).5(C3^2:C4)288,421
(C2×C4).6(C32⋊C4) = (C3×C12)⋊4C8φ: C32⋊C4/C3⋊S3C2 ⊆ Aut C2×C496(C2xC4).6(C3^2:C4)288,424
(C2×C4).7(C32⋊C4) = C2×C32⋊M4(2)φ: C32⋊C4/C3⋊S3C2 ⊆ Aut C2×C448(C2xC4).7(C3^2:C4)288,930
(C2×C4).8(C32⋊C4) = C3⋊S3⋊M4(2)φ: C32⋊C4/C3⋊S3C2 ⊆ Aut C2×C4244(C2xC4).8(C3^2:C4)288,931
(C2×C4).9(C32⋊C4) = C2×C322C16central extension (φ=1)96(C2xC4).9(C3^2:C4)288,420
(C2×C4).10(C32⋊C4) = C4×C322C8central extension (φ=1)96(C2xC4).10(C3^2:C4)288,423
(C2×C4).11(C32⋊C4) = C2×C3⋊S33C8central extension (φ=1)48(C2xC4).11(C3^2:C4)288,929

׿
×
𝔽