# Extensions 1→N→G→Q→1 with N=Q8×C32 and Q=C4

Direct product G=N×Q with N=Q8×C32 and Q=C4
dρLabelID
Q8×C3×C12288Q8xC3xC12288,816

Semidirect products G=N:Q with N=Q8×C32 and Q=C4
extensionφ:Q→Out NdρLabelID
(Q8×C32)⋊1C4 = C3⋊S3.5Q16φ: C4/C1C4 ⊆ Out Q8×C32488-(Q8xC3^2):1C4288,432
(Q8×C32)⋊2C4 = C327C4≀C2φ: C4/C1C4 ⊆ Out Q8×C32488+(Q8xC3^2):2C4288,433
(Q8×C32)⋊3C4 = Q8×C32⋊C4φ: C4/C1C4 ⊆ Out Q8×C32488-(Q8xC3^2):3C4288,938
(Q8×C32)⋊4C4 = C3×Q82Dic3φ: C4/C2C2 ⊆ Out Q8×C3296(Q8xC3^2):4C4288,269
(Q8×C32)⋊5C4 = C3×Q83Dic3φ: C4/C2C2 ⊆ Out Q8×C32484(Q8xC3^2):5C4288,271
(Q8×C32)⋊6C4 = C62.117D4φ: C4/C2C2 ⊆ Out Q8×C32288(Q8xC3^2):6C4288,310
(Q8×C32)⋊7C4 = C62.39D4φ: C4/C2C2 ⊆ Out Q8×C3272(Q8xC3^2):7C4288,312
(Q8×C32)⋊8C4 = C3×Q8×Dic3φ: C4/C2C2 ⊆ Out Q8×C3296(Q8xC3^2):8C4288,716
(Q8×C32)⋊9C4 = Q8×C3⋊Dic3φ: C4/C2C2 ⊆ Out Q8×C32288(Q8xC3^2):9C4288,802
(Q8×C32)⋊10C4 = C32×Q8⋊C4φ: C4/C2C2 ⊆ Out Q8×C32288(Q8xC3^2):10C4288,321
(Q8×C32)⋊11C4 = C32×C4≀C2φ: C4/C2C2 ⊆ Out Q8×C3272(Q8xC3^2):11C4288,322

Non-split extensions G=N.Q with N=Q8×C32 and Q=C4
extensionφ:Q→Out NdρLabelID
(Q8×C32).C4 = C12⋊S3.C4φ: C4/C1C4 ⊆ Out Q8×C32488+(Q8xC3^2).C4288,937
(Q8×C32).2C4 = C3×D4.Dic3φ: C4/C2C2 ⊆ Out Q8×C32484(Q8xC3^2).2C4288,719
(Q8×C32).3C4 = D4.(C3⋊Dic3)φ: C4/C2C2 ⊆ Out Q8×C32144(Q8xC3^2).3C4288,805
(Q8×C32).4C4 = C32×C8○D4φ: trivial image144(Q8xC3^2).4C4288,828

׿
×
𝔽