Extensions 1→N→G→Q→1 with N=C₂×C₅₆ and Q=C₂

Direct product G=N×Q with N=C₂×C₅₆ and Q=C₂

		d	ρ	Label	ID
C₂²×C₅₆		224		C2^2xC56	224,164

Semidirect products G=N:Q with N=C₂×C₅₆ and Q=C₂

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂×C₅₆)⋊₁C₂ = D₁₄⋊C₈	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₅₆	112		(C2xC56):1C2	224,26
(C₂×C₅₆)⋊₂C₂ = C₂.D₅₆	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₅₆	112		(C2xC56):2C2	224,27
(C₂×C₅₆)⋊₃C₂ = C₇×C₂²⋊C₈	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₅₆	112		(C2xC56):3C2	224,47
(C₂×C₅₆)⋊₄C₂ = C₇×D₄⋊C₄	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₅₆	112		(C2xC56):4C2	224,51
(C₂×C₅₆)⋊₅C₂ = C₂×D₅₆	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₅₆	112		(C2xC56):5C2	224,98
(C₂×C₅₆)⋊₆C₂ = D₅₆⋊₇C₂	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₅₆	112	2	(C2xC56):6C2	224,99
(C₂×C₅₆)⋊₇C₂ = C₂×C₅₆⋊C₂	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₅₆	112		(C2xC56):7C2	224,97
(C₂×C₅₆)⋊₈C₂ = D₇×C₂×C₈	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₅₆	112		(C2xC56):8C2	224,94
(C₂×C₅₆)⋊₉C₂ = C₂×C₈⋊D₇	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₅₆	112		(C2xC56):9C2	224,95
(C₂×C₅₆)⋊₁₀C₂ = D₂₈.₂C₄	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₅₆	112	2	(C2xC56):10C2	224,96
(C₂×C₅₆)⋊₁₁C₂ = C₁₄×D₈	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₅₆	112		(C2xC56):11C2	224,167
(C₂×C₅₆)⋊₁₂C₂ = C₇×C₄○D₈	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₅₆	112	2	(C2xC56):12C2	224,170
(C₂×C₅₆)⋊₁₃C₂ = C₁₄×SD₁₆	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₅₆	112		(C2xC56):13C2	224,168
(C₂×C₅₆)⋊₁₄C₂ = C₁₄×M₄(2)	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₅₆	112		(C2xC56):14C2	224,165
(C₂×C₅₆)⋊₁₅C₂ = C₇×C₈○D₄	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₅₆	112	2	(C2xC56):15C2	224,166

Non-split extensions G=N.Q with N=C₂×C₅₆ and Q=C₂

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂×C₅₆).₁C₂ = Dic₇⋊C₈	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₅₆	224		(C2xC56).1C2	224,20
(C₂×C₅₆).₂C₂ = C₂₈.₄₄D₄	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₅₆	224		(C2xC56).2C2	224,22
(C₂×C₅₆).₃C₂ = C₇×Q₈⋊C₄	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₅₆	224		(C2xC56).3C2	224,52
(C₂×C₅₆).₄C₂ = C₇×C₄⋊C₈	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₅₆	224		(C2xC56).4C2	224,54
(C₂×C₅₆).₅C₂ = C₅₆⋊₁C₄	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₅₆	224		(C2xC56).5C2	224,24
(C₂×C₅₆).₆C₂ = C₂×Dic₂₈	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₅₆	224		(C2xC56).6C2	224,100
(C₂×C₅₆).₇C₂ = C₅₆.C₄	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₅₆	112	2	(C2xC56).7C2	224,25
(C₂×C₅₆).₈C₂ = C₈⋊Dic₇	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₅₆	224		(C2xC56).8C2	224,23
(C₂×C₅₆).₉C₂ = C₂×C₇⋊C₁₆	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₅₆	224		(C2xC56).9C2	224,17
(C₂×C₅₆).₁₀C₂ = C₂₈.C₈	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₅₆	112	2	(C2xC56).10C2	224,18
(C₂×C₅₆).₁₁C₂ = C₈×Dic₇	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₅₆	224		(C2xC56).11C2	224,19
(C₂×C₅₆).₁₂C₂ = C₅₆⋊C₄	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₅₆	224		(C2xC56).12C2	224,21
(C₂×C₅₆).₁₃C₂ = C₇×C₂.D₈	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₅₆	224		(C2xC56).13C2	224,56
(C₂×C₅₆).₁₄C₂ = C₁₄×Q₁₆	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₅₆	224		(C2xC56).14C2	224,169
(C₂×C₅₆).₁₅C₂ = C₇×C₈.C₄	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₅₆	112	2	(C2xC56).15C2	224,57
(C₂×C₅₆).₁₆C₂ = C₇×C₄.Q₈	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₅₆	224		(C2xC56).16C2	224,55
(C₂×C₅₆).₁₇C₂ = C₇×C₈⋊C₄	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₅₆	224		(C2xC56).17C2	224,46
(C₂×C₅₆).₁₈C₂ = C₇×M₅(2)	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₅₆	112	2	(C2xC56).18C2	224,59

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