Extensions 1→N→G→Q→1 with N=C₂³×C₄ and Q=C₂

Direct product G=N×Q with N=C₂³×C₄ and Q=C₂

		d	ρ	Label	ID
C₂⁴×C₄		64		C2^4xC4	64,260

Semidirect products G=N:Q with N=C₂³×C₄ and Q=C₂

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂³×C₄)⋊₁C₂ = C₂³.₂₃D₄	φ: C₂/C₁ → C₂ ⊆ Aut C₂³×C₄	32		(C2^3xC4):1C2	64,67
(C₂³×C₄)⋊₂C₂ = C₂²×C₂²⋊C₄	φ: C₂/C₁ → C₂ ⊆ Aut C₂³×C₄	32		(C2^3xC4):2C2	64,193
(C₂³×C₄)⋊₃C₂ = C₂×C₄×D₄	φ: C₂/C₁ → C₂ ⊆ Aut C₂³×C₄	32		(C2^3xC4):3C2	64,196
(C₂³×C₄)⋊₄C₂ = C₂×C₂².D₄	φ: C₂/C₁ → C₂ ⊆ Aut C₂³×C₄	32		(C2^3xC4):4C2	64,205
(C₂³×C₄)⋊₅C₂ = C₂×C₄⋊D₄	φ: C₂/C₁ → C₂ ⊆ Aut C₂³×C₄	32		(C2^3xC4):5C2	64,203
(C₂³×C₄)⋊₆C₂ = C₂².₁₉C₂⁴	φ: C₂/C₁ → C₂ ⊆ Aut C₂³×C₄	16		(C2^3xC4):6C2	64,206
(C₂³×C₄)⋊₇C₂ = D₄×C₂³	φ: C₂/C₁ → C₂ ⊆ Aut C₂³×C₄	32		(C2^3xC4):7C2	64,261
(C₂³×C₄)⋊₈C₂ = C₂²×C₄○D₄	φ: C₂/C₁ → C₂ ⊆ Aut C₂³×C₄	32		(C2^3xC4):8C2	64,263

Non-split extensions G=N.Q with N=C₂³×C₄ and Q=C₂

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂³×C₄).₁C₂ = C₂×C₂.C₄²	φ: C₂/C₁ → C₂ ⊆ Aut C₂³×C₄	64		(C2^3xC4).1C2	64,56
(C₂³×C₄).₂C₂ = C₄×C₂²⋊C₄	φ: C₂/C₁ → C₂ ⊆ Aut C₂³×C₄	32		(C2^3xC4).2C2	64,58
(C₂³×C₄).₃C₂ = C₂³.₃₄D₄	φ: C₂/C₁ → C₂ ⊆ Aut C₂³×C₄	32		(C2^3xC4).3C2	64,62
(C₂³×C₄).₄C₂ = C₂³.₈Q₈	φ: C₂/C₁ → C₂ ⊆ Aut C₂³×C₄	32		(C2^3xC4).4C2	64,66
(C₂³×C₄).₅C₂ = C₂×C₂²⋊C₈	φ: C₂/C₁ → C₂ ⊆ Aut C₂³×C₄	32		(C2^3xC4).5C2	64,87
(C₂³×C₄).₆C₂ = C₂³.₇Q₈	φ: C₂/C₁ → C₂ ⊆ Aut C₂³×C₄	32		(C2^3xC4).6C2	64,61
(C₂³×C₄).₇C₂ = C₂⁴.₄C₄	φ: C₂/C₁ → C₂ ⊆ Aut C₂³×C₄	16		(C2^3xC4).7C2	64,88
(C₂³×C₄).₈C₂ = C₂²×C₄⋊C₄	φ: C₂/C₁ → C₂ ⊆ Aut C₂³×C₄	64		(C2^3xC4).8C2	64,194
(C₂³×C₄).₉C₂ = C₂×C₄²⋊C₂	φ: C₂/C₁ → C₂ ⊆ Aut C₂³×C₄	32		(C2^3xC4).9C2	64,195
(C₂³×C₄).₁₀C₂ = C₂×C₂²⋊Q₈	φ: C₂/C₁ → C₂ ⊆ Aut C₂³×C₄	32		(C2^3xC4).10C2	64,204
(C₂³×C₄).₁₁C₂ = C₂²×M₄(2)	φ: C₂/C₁ → C₂ ⊆ Aut C₂³×C₄	32		(C2^3xC4).11C2	64,247
(C₂³×C₄).₁₂C₂ = Q₈×C₂³	φ: C₂/C₁ → C₂ ⊆ Aut C₂³×C₄	64		(C2^3xC4).12C2	64,262

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