Extensions 1→N→G→Q→1 with N=C₄×C₅₆ and Q=C₂

Direct product G=N×Q with N=C₄×C₅₆ and Q=C₂

		d	ρ	Label	ID
C₂×C₄×C₅₆		448		C2xC4xC56	448,810

Semidirect products G=N:Q with N=C₄×C₅₆ and Q=C₂

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₄×C₅₆)⋊₁C₂ = C₄.₁₇D₅₆	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₆	224		(C4xC56):1C2	448,16
(C₄×C₅₆)⋊₂C₂ = C₇×D₄⋊C₈	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₆	224		(C4xC56):2C2	448,129
(C₄×C₅₆)⋊₃C₂ = C₄².₂₈₂D₁₄	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₆	224		(C4xC56):3C2	448,219
(C₄×C₅₆)⋊₄C₂ = C₄².₂₄₃D₁₄	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₆	224		(C4xC56):4C2	448,224
(C₄×C₅₆)⋊₅C₂ = C₄.₅D₅₆	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₆	224		(C4xC56):5C2	448,228
(C₄×C₅₆)⋊₆C₂ = C₄².₂₆₄D₁₄	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₆	224		(C4xC56):6C2	448,231
(C₄×C₅₆)⋊₇C₂ = C₇×C₄².₁₂C₄	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₆	224		(C4xC56):7C2	448,839
(C₄×C₅₆)⋊₈C₂ = C₇×C₄².₇C₂²	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₆	224		(C4xC56):8C2	448,841
(C₄×C₅₆)⋊₉C₂ = D₄×C₅₆	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₆	224		(C4xC56):9C2	448,842
(C₄×C₅₆)⋊₁₀C₂ = C₇×C₄.₄D₈	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₆	224		(C4xC56):10C2	448,894
(C₄×C₅₆)⋊₁₁C₂ = C₇×C₄².₇₈C₂²	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₆	224		(C4xC56):11C2	448,896
(C₄×C₅₆)⋊₁₂C₂ = C₄×D₅₆	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₆	224		(C4xC56):12C2	448,226
(C₄×C₅₆)⋊₁₃C₂ = C₂₈⋊₄D₈	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₆	224		(C4xC56):13C2	448,229
(C₄×C₅₆)⋊₁₄C₂ = C₈.₈D₂₈	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₆	224		(C4xC56):14C2	448,230
(C₄×C₅₆)⋊₁₅C₂ = D₅₆⋊₁₁C₄	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₆	112	2	(C4xC56):15C2	448,234
(C₄×C₅₆)⋊₁₆C₂ = C₄×C₅₆⋊C₂	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₆	224		(C4xC56):16C2	448,225
(C₄×C₅₆)⋊₁₇C₂ = C₈⋊₅D₂₈	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₆	224		(C4xC56):17C2	448,227
(C₄×C₅₆)⋊₁₈C₂ = D₇×C₄×C₈	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₆	224		(C4xC56):18C2	448,218
(C₄×C₅₆)⋊₁₉C₂ = C₈×D₂₈	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₆	224		(C4xC56):19C2	448,220
(C₄×C₅₆)⋊₂₀C₂ = C₄×C₈⋊D₇	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₆	224		(C4xC56):20C2	448,221
(C₄×C₅₆)⋊₂₁C₂ = C₈⋊₆D₂₈	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₆	224		(C4xC56):21C2	448,222
(C₄×C₅₆)⋊₂₂C₂ = D₁₄.C₄²	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₆	224		(C4xC56):22C2	448,223
(C₄×C₅₆)⋊₂₃C₂ = D₈×C₂₈	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₆	224		(C4xC56):23C2	448,845
(C₄×C₅₆)⋊₂₄C₂ = C₇×C₈⋊₄D₄	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₆	224		(C4xC56):24C2	448,901
(C₄×C₅₆)⋊₂₅C₂ = C₇×C₈.₁₂D₄	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₆	224		(C4xC56):25C2	448,903
(C₄×C₅₆)⋊₂₆C₂ = C₇×C₈○D₈	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₆	112	2	(C4xC56):26C2	448,851
(C₄×C₅₆)⋊₂₇C₂ = SD₁₆×C₂₈	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₆	224		(C4xC56):27C2	448,846
(C₄×C₅₆)⋊₂₈C₂ = C₇×C₈⋊₅D₄	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₆	224		(C4xC56):28C2	448,900
(C₄×C₅₆)⋊₂₉C₂ = M₄(2)×C₂₈	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₆	224		(C4xC56):29C2	448,812
(C₄×C₅₆)⋊₃₀C₂ = C₇×C₈○₂M₄(2)	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₆	224		(C4xC56):30C2	448,813
(C₄×C₅₆)⋊₃₁C₂ = C₇×C₈⋊₆D₄	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₆	224		(C4xC56):31C2	448,844

Non-split extensions G=N.Q with N=C₄×C₅₆ and Q=C₂

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₄×C₅₆).₁C₂ = C₄².₂₇₉D₁₄	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₆	448		(C4xC56).1C2	448,11
(C₄×C₅₆).₂C₂ = C₄.₈Dic₂₈	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₆	448		(C4xC56).2C2	448,13
(C₄×C₅₆).₃C₂ = C₇×Q₈⋊C₈	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₆	448		(C4xC56).3C2	448,130
(C₄×C₅₆).₄C₂ = C₇×C₄⋊C₁₆	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₆	448		(C4xC56).4C2	448,167
(C₄×C₅₆).₅C₂ = C₂₈.₁₄Q₁₆	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₆	448		(C4xC56).5C2	448,215
(C₄×C₅₆).₆C₂ = Q₈×C₅₆	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₆	448		(C4xC56).6C2	448,853
(C₄×C₅₆).₇C₂ = C₇×C₄.SD₁₆	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₆	448		(C4xC56).7C2	448,895
(C₄×C₅₆).₈C₂ = C₅₆⋊₁C₈	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₆	448		(C4xC56).8C2	448,15
(C₄×C₅₆).₉C₂ = C₅₆⋊₈Q₈	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₆	448		(C4xC56).9C2	448,216
(C₄×C₅₆).₁₀C₂ = C₄×Dic₂₈	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₆	448		(C4xC56).10C2	448,232
(C₄×C₅₆).₁₁C₂ = C₂₈⋊₄Q₁₆	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₆	448		(C4xC56).11C2	448,233
(C₄×C₅₆).₁₂C₂ = C₅₆.₁₃Q₈	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₆	448		(C4xC56).12C2	448,217
(C₄×C₅₆).₁₃C₂ = C₅₆.₁₆Q₈	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₆	112	2	(C4xC56).13C2	448,20
(C₄×C₅₆).₁₄C₂ = C₅₆⋊₂C₈	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₆	448		(C4xC56).14C2	448,14
(C₄×C₅₆).₁₅C₂ = C₅₆⋊₉Q₈	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₆	448		(C4xC56).15C2	448,214
(C₄×C₅₆).₁₆C₂ = C₈×C₇⋊C₈	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₆	448		(C4xC56).16C2	448,10
(C₄×C₅₆).₁₇C₂ = C₅₆⋊C₈	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₆	448		(C4xC56).17C2	448,12
(C₄×C₅₆).₁₈C₂ = C₄×C₇⋊C₁₆	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₆	448		(C4xC56).18C2	448,17
(C₄×C₅₆).₁₉C₂ = C₅₆.C₈	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₆	448		(C4xC56).19C2	448,18
(C₄×C₅₆).₂₀C₂ = C₂₈⋊C₁₆	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₆	448		(C4xC56).20C2	448,19
(C₄×C₅₆).₂₁C₂ = C₈×Dic₁₄	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₆	448		(C4xC56).21C2	448,212
(C₄×C₅₆).₂₂C₂ = C₅₆⋊₁₁Q₈	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₆	448		(C4xC56).22C2	448,213
(C₄×C₅₆).₂₃C₂ = C₇×C₈⋊₁C₈	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₆	448		(C4xC56).23C2	448,139
(C₄×C₅₆).₂₄C₂ = Q₁₆×C₂₈	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₆	448		(C4xC56).24C2	448,847
(C₄×C₅₆).₂₅C₂ = C₇×C₄⋊Q₁₆	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₆	448		(C4xC56).25C2	448,902
(C₄×C₅₆).₂₆C₂ = C₇×C₈⋊₂Q₈	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₆	448		(C4xC56).26C2	448,908
(C₄×C₅₆).₂₇C₂ = C₇×C₈.₅Q₈	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₆	448		(C4xC56).27C2	448,907
(C₄×C₅₆).₂₈C₂ = C₇×C₈.C₈	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₆	112	2	(C4xC56).28C2	448,168
(C₄×C₅₆).₂₉C₂ = C₇×C₈⋊₂C₈	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₆	448		(C4xC56).29C2	448,138
(C₄×C₅₆).₃₀C₂ = C₇×C₈⋊₃Q₈	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₆	448		(C4xC56).30C2	448,906
(C₄×C₅₆).₃₁C₂ = C₇×C₈⋊C₈	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₆	448		(C4xC56).31C2	448,126
(C₄×C₅₆).₃₂C₂ = C₇×C₁₆⋊₅C₄	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₆	448		(C4xC56).32C2	448,150
(C₄×C₅₆).₃₃C₂ = C₇×C₈⋊₄Q₈	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₅₆	448		(C4xC56).33C2	448,854

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Extensions 1→N→G→Q→1 with N=C4×C56 and Q=C2

Extensions 1→N→G→Q→1 with N=C₄×C₅₆ and Q=C₂