Extensions 1→N→G→Q→1 with N=C₂×C₄² and Q=C₂

Direct product G=N×Q with N=C₂×C₄² and Q=C₂

		d	ρ	Label	ID
C₂²×C₄²		64		C2^2xC4^2	64,192

Semidirect products G=N:Q with N=C₂×C₄² and Q=C₂

extension	φ:Q→Aut N	d	Label	ID
(C₂×C₄²)⋊₁C₂ = C₄×C₂²⋊C₄	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₄²	32	(C2xC4^2):1C2	64,58
(C₂×C₄²)⋊₂C₂ = C₂⁴.C₂²	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₄²	32	(C2xC4^2):2C2	64,69
(C₂×C₄²)⋊₃C₂ = C₂×C₄²⋊C₂	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₄²	32	(C2xC4^2):3C2	64,195
(C₂×C₄²)⋊₄C₂ = C₂×C₄²⋊₂C₂	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₄²	32	(C2xC4^2):4C2	64,209
(C₂×C₄²)⋊₅C₂ = C₂⁴.₃C₂²	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₄²	32	(C2xC4^2):5C2	64,71
(C₂×C₄²)⋊₆C₂ = C₂×C₄≀C₂	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₄²	16	(C2xC4^2):6C2	64,101
(C₂×C₄²)⋊₇C₂ = C₂×C₄×D₄	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₄²	32	(C2xC4^2):7C2	64,196
(C₂×C₄²)⋊₈C₂ = C₄×C₄○D₄	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₄²	32	(C2xC4^2):8C2	64,198
(C₂×C₄²)⋊₉C₂ = C₂×C₄.₄D₄	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₄²	32	(C2xC4^2):9C2	64,207
(C₂×C₄²)⋊₁₀C₂ = C₂³.₃₆C₂³	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₄²	32	(C2xC4^2):10C2	64,210
(C₂×C₄²)⋊₁₁C₂ = C₂×C₄⋊₁D₄	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₄²	32	(C2xC4^2):11C2	64,211
(C₂×C₄²)⋊₁₂C₂ = C₂².₂₆C₂⁴	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₄²	32	(C2xC4^2):12C2	64,213

Non-split extensions G=N.Q with N=C₂×C₄² and Q=C₂

extension	φ:Q→Aut N	d	Label	ID
(C₂×C₄²).₁C₂ = C₂².₇C₄²	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₄²	64	(C2xC4^2).1C2	64,17
(C₂×C₄²).₂C₂ = C₄²⋊₄C₄	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₄²	64	(C2xC4^2).2C2	64,57
(C₂×C₄²).₃C₂ = C₄²⋊₅C₄	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₄²	64	(C2xC4^2).3C2	64,64
(C₂×C₄²).₄C₂ = C₂³.₆₃C₂³	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₄²	64	(C2xC4^2).4C2	64,68
(C₂×C₄²).₅C₂ = C₂×C₈⋊C₄	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₄²	64	(C2xC4^2).5C2	64,84
(C₂×C₄²).₆C₂ = C₄²⋊₆C₄	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₄²	16	(C2xC4^2).6C2	64,20
(C₂×C₄²).₇C₂ = C₄×C₄⋊C₄	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₄²	64	(C2xC4^2).7C2	64,59
(C₂×C₄²).₈C₂ = C₄²⋊₈C₄	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₄²	64	(C2xC4^2).8C2	64,63
(C₂×C₄²).₉C₂ = C₄²⋊₉C₄	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₄²	64	(C2xC4^2).9C2	64,65
(C₂×C₄²).₁₀C₂ = C₂³.₆₅C₂³	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₄²	64	(C2xC4^2).10C2	64,70
(C₂×C₄²).₁₁C₂ = C₂³.₆₇C₂³	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₄²	64	(C2xC4^2).11C2	64,72
(C₂×C₄²).₁₂C₂ = C₄×M₄(2)	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₄²	32	(C2xC4^2).12C2	64,85
(C₂×C₄²).₁₃C₂ = C₂×C₄⋊C₈	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₄²	64	(C2xC4^2).13C2	64,103
(C₂×C₄²).₁₄C₂ = C₄⋊M₄(2)	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₄²	32	(C2xC4^2).14C2	64,104
(C₂×C₄²).₁₅C₂ = C₄².₁₂C₄	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₄²	32	(C2xC4^2).15C2	64,112
(C₂×C₄²).₁₆C₂ = C₄².₆C₄	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₄²	32	(C2xC4^2).16C2	64,113
(C₂×C₄²).₁₇C₂ = C₂×C₄×Q₈	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₄²	64	(C2xC4^2).17C2	64,197
(C₂×C₄²).₁₈C₂ = C₂×C₄².C₂	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₄²	64	(C2xC4^2).18C2	64,208
(C₂×C₄²).₁₉C₂ = C₂×C₄⋊Q₈	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₄²	64	(C2xC4^2).19C2	64,212
(C₂×C₄²).₂₀C₂ = C₂³.₃₇C₂³	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₄²	32	(C2xC4^2).20C2	64,214

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Extensions 1→N→G→Q→1 with N=C2×C42 and Q=C2

Extensions 1→N→G→Q→1 with N=C₂×C₄² and Q=C₂