Extensions 1→N→G→Q→1 with N=C₇×M₅(2) and Q=C₂

Direct product G=N×Q with N=C₇×M₅(2) and Q=C₂

		d	ρ	Label	ID
C₁₄×M₅(2)		224		C14xM5(2)	448,911

Semidirect products G=N:Q with N=C₇×M₅(2) and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
(C₇×M₅(2))⋊₁C₂ = C₁₆⋊D₁₄	φ: C₂/C₁ → C₂ ⊆ Out C₇×M₅(2)	112	4+	(C7xM5(2)):1C2	448,442
(C₇×M₅(2))⋊₂C₂ = C₁₆.D₁₄	φ: C₂/C₁ → C₂ ⊆ Out C₇×M₅(2)	224	4-	(C7xM5(2)):2C2	448,443
(C₇×M₅(2))⋊₃C₂ = C₇×C₁₆⋊C₂²	φ: C₂/C₁ → C₂ ⊆ Out C₇×M₅(2)	112	4	(C7xM5(2)):3C2	448,917
(C₇×M₅(2))⋊₄C₂ = C₇×Q₃₂⋊C₂	φ: C₂/C₁ → C₂ ⊆ Out C₇×M₅(2)	224	4	(C7xM5(2)):4C2	448,918
(C₇×M₅(2))⋊₅C₂ = D₇×M₅(2)	φ: C₂/C₁ → C₂ ⊆ Out C₇×M₅(2)	112	4	(C7xM5(2)):5C2	448,440
(C₇×M₅(2))⋊₆C₂ = C₁₆.₁₂D₁₄	φ: C₂/C₁ → C₂ ⊆ Out C₇×M₅(2)	224	4	(C7xM5(2)):6C2	448,441
(C₇×M₅(2))⋊₇C₂ = M₅(2)⋊D₇	φ: C₂/C₁ → C₂ ⊆ Out C₇×M₅(2)	112	4	(C7xM5(2)):7C2	448,71
(C₇×M₅(2))⋊₈C₂ = Dic₁₄.C₈	φ: C₂/C₁ → C₂ ⊆ Out C₇×M₅(2)	224	4	(C7xM5(2)):8C2	448,72
(C₇×M₅(2))⋊₉C₂ = C₂₈.₃D₈	φ: C₂/C₁ → C₂ ⊆ Out C₇×M₅(2)	112	4+	(C7xM5(2)):9C2	448,73
(C₇×M₅(2))⋊₁₀C₂ = D₅₆⋊₂C₄	φ: C₂/C₁ → C₂ ⊆ Out C₇×M₅(2)	112	4	(C7xM5(2)):10C2	448,75
(C₇×M₅(2))⋊₁₁C₂ = C₇×C₂³.C₈	φ: C₂/C₁ → C₂ ⊆ Out C₇×M₅(2)	112	4	(C7xM5(2)):11C2	448,153
(C₇×M₅(2))⋊₁₂C₂ = C₇×D₄.C₈	φ: C₂/C₁ → C₂ ⊆ Out C₇×M₅(2)	224	2	(C7xM5(2)):12C2	448,154
(C₇×M₅(2))⋊₁₃C₂ = C₇×D₈⋊₂C₄	φ: C₂/C₁ → C₂ ⊆ Out C₇×M₅(2)	112	4	(C7xM5(2)):13C2	448,164
(C₇×M₅(2))⋊₁₄C₂ = C₇×M₅(2)⋊C₂	φ: C₂/C₁ → C₂ ⊆ Out C₇×M₅(2)	112	4	(C7xM5(2)):14C2	448,165
(C₇×M₅(2))⋊₁₅C₂ = C₇×D₄○C₁₆	φ: trivial image	224	2	(C7xM5(2)):15C2	448,912

Non-split extensions G=N.Q with N=C₇×M₅(2) and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
(C₇×M₅(2)).₁C₂ = C₁₆⋊Dic₇	φ: C₂/C₁ → C₂ ⊆ Out C₇×M₅(2)	112	4	(C7xM5(2)).1C2	448,70
(C₇×M₅(2)).₂C₂ = C₁₁₂⋊C₄	φ: C₂/C₁ → C₂ ⊆ Out C₇×M₅(2)	112	4	(C7xM5(2)).2C2	448,69
(C₇×M₅(2)).₃C₂ = C₇×C₈.Q₈	φ: C₂/C₁ → C₂ ⊆ Out C₇×M₅(2)	112	4	(C7xM5(2)).3C2	448,169
(C₇×M₅(2)).₄C₂ = C₅₆.₉Q₈	φ: C₂/C₁ → C₂ ⊆ Out C₇×M₅(2)	112	4	(C7xM5(2)).4C2	448,68
(C₇×M₅(2)).₅C₂ = C₂₈.₄D₈	φ: C₂/C₁ → C₂ ⊆ Out C₇×M₅(2)	224	4-	(C7xM5(2)).5C2	448,74
(C₇×M₅(2)).₆C₂ = C₇×C₁₆⋊C₄	φ: C₂/C₁ → C₂ ⊆ Out C₇×M₅(2)	112	4	(C7xM5(2)).6C2	448,151
(C₇×M₅(2)).₇C₂ = C₇×C₈.₁₇D₄	φ: C₂/C₁ → C₂ ⊆ Out C₇×M₅(2)	224	4	(C7xM5(2)).7C2	448,166
(C₇×M₅(2)).₈C₂ = C₇×C₈.C₈	φ: C₂/C₁ → C₂ ⊆ Out C₇×M₅(2)	112	2	(C7xM5(2)).8C2	448,168

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