Extensions 1→N→G→Q→1 with N=C₂×C₄² and Q=D₇

Direct product G=N×Q with N=C₂×C₄² and Q=D₇

		d	ρ	Label	ID
D₇×C₂×C₄²		224		D7xC2xC4^2	448,924

Semidirect products G=N:Q with N=C₂×C₄² and Q=D₇

extension	φ:Q→Aut N	d	Label	ID
(C₂×C₄²)⋊₁D₇ = C₄×D₁₄⋊C₄	φ: D₇/C₇ → C₂ ⊆ Aut C₂×C₄²	224	(C2xC4^2):1D7	448,472
(C₂×C₄²)⋊₂D₇ = (C₂×C₄²)⋊D₇	φ: D₇/C₇ → C₂ ⊆ Aut C₂×C₄²	224	(C2xC4^2):2D7	448,474
(C₂×C₄²)⋊₃D₇ = C₂×C₄²⋊D₇	φ: D₇/C₇ → C₂ ⊆ Aut C₂×C₄²	224	(C2xC4^2):3D7	448,925
(C₂×C₄²)⋊₄D₇ = C₂×C₄²⋊₂D₇	φ: D₇/C₇ → C₂ ⊆ Aut C₂×C₄²	224	(C2xC4^2):4D7	448,931
(C₂×C₄²)⋊₅D₇ = C₂×Dic₁₄⋊C₄	φ: D₇/C₇ → C₂ ⊆ Aut C₂×C₄²	112	(C2xC4^2):5D7	448,461
(C₂×C₄²)⋊₆D₇ = (C₂×C₄)⋊₆D₂₈	φ: D₇/C₇ → C₂ ⊆ Aut C₂×C₄²	224	(C2xC4^2):6D7	448,473
(C₂×C₄²)⋊₇D₇ = C₂×C₄×D₂₈	φ: D₇/C₇ → C₂ ⊆ Aut C₂×C₄²	224	(C2xC4^2):7D7	448,926
(C₂×C₄²)⋊₈D₇ = C₄×C₄○D₂₈	φ: D₇/C₇ → C₂ ⊆ Aut C₂×C₄²	224	(C2xC4^2):8D7	448,927
(C₂×C₄²)⋊₉D₇ = C₂×C₂₈⋊₄D₄	φ: D₇/C₇ → C₂ ⊆ Aut C₂×C₄²	224	(C2xC4^2):9D7	448,928
(C₂×C₄²)⋊₁₀D₇ = C₂×C₄.D₂₈	φ: D₇/C₇ → C₂ ⊆ Aut C₂×C₄²	224	(C2xC4^2):10D7	448,929
(C₂×C₄²)⋊₁₁D₇ = C₄².₂₇₆D₁₄	φ: D₇/C₇ → C₂ ⊆ Aut C₂×C₄²	224	(C2xC4^2):11D7	448,930
(C₂×C₄²)⋊₁₂D₇ = C₄².₂₇₇D₁₄	φ: D₇/C₇ → C₂ ⊆ Aut C₂×C₄²	224	(C2xC4^2):12D7	448,932

Non-split extensions G=N.Q with N=C₂×C₄² and Q=D₇

extension	φ:Q→Aut N	d	Label	ID
(C₂×C₄²).₁D₇ = (C₂×C₂₈)⋊₃C₈	φ: D₇/C₇ → C₂ ⊆ Aut C₂×C₄²	448	(C2xC4^2).1D7	448,81
(C₂×C₄²).₂D₇ = C₂×C₄².D₇	φ: D₇/C₇ → C₂ ⊆ Aut C₂×C₄²	448	(C2xC4^2).2D7	448,455
(C₂×C₄²).₃D₇ = C₄×Dic₇⋊C₄	φ: D₇/C₇ → C₂ ⊆ Aut C₂×C₄²	448	(C2xC4^2).3D7	448,465
(C₂×C₄²).₄D₇ = C₄²⋊₄Dic₇	φ: D₇/C₇ → C₂ ⊆ Aut C₂×C₄²	448	(C2xC4^2).4D7	448,466
(C₂×C₄²).₅D₇ = (C₂×C₄²).D₇	φ: D₇/C₇ → C₂ ⊆ Aut C₂×C₄²	448	(C2xC4^2).5D7	448,467
(C₂×C₄²).₆D₇ = C₄²⋊₅Dic₇	φ: D₇/C₇ → C₂ ⊆ Aut C₂×C₄²	448	(C2xC4^2).6D7	448,471
(C₂×C₄²).₇D₇ = C₂₈.₈C₄²	φ: D₇/C₇ → C₂ ⊆ Aut C₂×C₄²	112	(C2xC4^2).7D7	448,80
(C₂×C₄²).₈D₇ = C₄×C₄.Dic₇	φ: D₇/C₇ → C₂ ⊆ Aut C₂×C₄²	224	(C2xC4^2).8D7	448,456
(C₂×C₄²).₉D₇ = C₂×C₂₈⋊C₈	φ: D₇/C₇ → C₂ ⊆ Aut C₂×C₄²	448	(C2xC4^2).9D7	448,457
(C₂×C₄²).₁₀D₇ = C₂₈⋊₇M₄(2)	φ: D₇/C₇ → C₂ ⊆ Aut C₂×C₄²	224	(C2xC4^2).10D7	448,458
(C₂×C₄²).₁₁D₇ = C₄².₆Dic₇	φ: D₇/C₇ → C₂ ⊆ Aut C₂×C₄²	224	(C2xC4^2).11D7	448,459
(C₂×C₄²).₁₂D₇ = C₄².₇Dic₇	φ: D₇/C₇ → C₂ ⊆ Aut C₂×C₄²	224	(C2xC4^2).12D7	448,460
(C₂×C₄²).₁₃D₇ = C₂₈⋊₄(C₄⋊C₄)	φ: D₇/C₇ → C₂ ⊆ Aut C₂×C₄²	448	(C2xC4^2).13D7	448,462
(C₂×C₄²).₁₄D₇ = (C₂×C₂₈)⋊₁₀Q₈	φ: D₇/C₇ → C₂ ⊆ Aut C₂×C₄²	448	(C2xC4^2).14D7	448,463
(C₂×C₄²).₁₅D₇ = C₄×C₄⋊Dic₇	φ: D₇/C₇ → C₂ ⊆ Aut C₂×C₄²	448	(C2xC4^2).15D7	448,468
(C₂×C₄²).₁₆D₇ = C₄²⋊₈Dic₇	φ: D₇/C₇ → C₂ ⊆ Aut C₂×C₄²	448	(C2xC4^2).16D7	448,469
(C₂×C₄²).₁₇D₇ = C₄²⋊₉Dic₇	φ: D₇/C₇ → C₂ ⊆ Aut C₂×C₄²	448	(C2xC4^2).17D7	448,470
(C₂×C₄²).₁₈D₇ = C₂×C₄×Dic₁₄	φ: D₇/C₇ → C₂ ⊆ Aut C₂×C₄²	448	(C2xC4^2).18D7	448,920
(C₂×C₄²).₁₉D₇ = C₂×C₂₈⋊₂Q₈	φ: D₇/C₇ → C₂ ⊆ Aut C₂×C₄²	448	(C2xC4^2).19D7	448,921
(C₂×C₄²).₂₀D₇ = C₂×C₂₈.₆Q₈	φ: D₇/C₇ → C₂ ⊆ Aut C₂×C₄²	448	(C2xC4^2).20D7	448,922
(C₂×C₄²).₂₁D₇ = C₄².₂₇₄D₁₄	φ: D₇/C₇ → C₂ ⊆ Aut C₂×C₄²	224	(C2xC4^2).21D7	448,923
(C₂×C₄²).₂₂D₇ = C₂×C₄×C₇⋊C₈	central extension (φ=1)	448	(C2xC4^2).22D7	448,454
(C₂×C₄²).₂₃D₇ = C₄²×Dic₇	central extension (φ=1)	448	(C2xC4^2).23D7	448,464

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Extensions 1→N→G→Q→1 with N=C2×C42 and Q=D7

Extensions 1→N→G→Q→1 with N=C₂×C₄² and Q=D₇