Extensions 1→N→G→Q→1 with N=C₇×M₄(2) and Q=C₂

Direct product G=N×Q with N=C₇×M₄(2) and Q=C₂

		d	ρ	Label	ID
C₁₄×M₄(2)		112		C14xM4(2)	224,165

Semidirect products G=N:Q with N=C₇×M₄(2) and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
(C₇×M₄(2))⋊₁C₂ = C₈⋊D₁₄	φ: C₂/C₁ → C₂ ⊆ Out C₇×M₄(2)	56	4+	(C7xM4(2)):1C2	224,103
(C₇×M₄(2))⋊₂C₂ = C₈.D₁₄	φ: C₂/C₁ → C₂ ⊆ Out C₇×M₄(2)	112	4-	(C7xM4(2)):2C2	224,104
(C₇×M₄(2))⋊₃C₂ = D₇×M₄(2)	φ: C₂/C₁ → C₂ ⊆ Out C₇×M₄(2)	56	4	(C7xM4(2)):3C2	224,101
(C₇×M₄(2))⋊₄C₂ = D₂₈.C₄	φ: C₂/C₁ → C₂ ⊆ Out C₇×M₄(2)	112	4	(C7xM4(2)):4C2	224,102
(C₇×M₄(2))⋊₅C₂ = C₇×C₈⋊C₂²	φ: C₂/C₁ → C₂ ⊆ Out C₇×M₄(2)	56	4	(C7xM4(2)):5C2	224,171
(C₇×M₄(2))⋊₆C₂ = C₇×C₈.C₂²	φ: C₂/C₁ → C₂ ⊆ Out C₇×M₄(2)	112	4	(C7xM4(2)):6C2	224,172
(C₇×M₄(2))⋊₇C₂ = C₂₈.₄₆D₄	φ: C₂/C₁ → C₂ ⊆ Out C₇×M₄(2)	56	4+	(C7xM4(2)):7C2	224,29
(C₇×M₄(2))⋊₈C₂ = D₂₈⋊₄C₄	φ: C₂/C₁ → C₂ ⊆ Out C₇×M₄(2)	56	4	(C7xM4(2)):8C2	224,31
(C₇×M₄(2))⋊₉C₂ = C₇×C₄.D₄	φ: C₂/C₁ → C₂ ⊆ Out C₇×M₄(2)	56	4	(C7xM4(2)):9C2	224,49
(C₇×M₄(2))⋊₁₀C₂ = C₇×C₄≀C₂	φ: C₂/C₁ → C₂ ⊆ Out C₇×M₄(2)	56	2	(C7xM4(2)):10C2	224,53
(C₇×M₄(2))⋊₁₁C₂ = C₇×C₈○D₄	φ: trivial image	112	2	(C7xM4(2)):11C2	224,166

Non-split extensions G=N.Q with N=C₇×M₄(2) and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
(C₇×M₄(2)).₁C₂ = C₂₈.₅₃D₄	φ: C₂/C₁ → C₂ ⊆ Out C₇×M₄(2)	112	4	(C7xM4(2)).1C2	224,28
(C₇×M₄(2)).₂C₂ = C₄.₁₂D₂₈	φ: C₂/C₁ → C₂ ⊆ Out C₇×M₄(2)	112	4-	(C7xM4(2)).2C2	224,30
(C₇×M₄(2)).₃C₂ = C₇×C₄.₁₀D₄	φ: C₂/C₁ → C₂ ⊆ Out C₇×M₄(2)	112	4	(C7xM4(2)).3C2	224,50
(C₇×M₄(2)).₄C₂ = C₇×C₈.C₄	φ: C₂/C₁ → C₂ ⊆ Out C₇×M₄(2)	112	2	(C7xM4(2)).4C2	224,57

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