Extensions 1→N→G→Q→1 with N=D₇×M₄(2) and Q=C₂

Direct product G=N×Q with N=D₇×M₄(2) and Q=C₂

		d	ρ	Label	ID
C₂×D₇×M₄(2)		112		C2xD7xM4(2)	448,1196

Semidirect products G=N:Q with N=D₇×M₄(2) and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
(D₇×M₄(2))⋊₁C₂ = D₇×C₈⋊C₂²	φ: C₂/C₁ → C₂ ⊆ Out D₇×M₄(2)	56	8+	(D7xM4(2)):1C2	448,1225
(D₇×M₄(2))⋊₂C₂ = SD₁₆⋊D₁₄	φ: C₂/C₁ → C₂ ⊆ Out D₇×M₄(2)	112	8-	(D7xM4(2)):2C2	448,1226
(D₇×M₄(2))⋊₃C₂ = D₇×C₈.C₂²	φ: C₂/C₁ → C₂ ⊆ Out D₇×M₄(2)	112	8-	(D7xM4(2)):3C2	448,1229
(D₇×M₄(2))⋊₄C₂ = D₅₆⋊C₂²	φ: C₂/C₁ → C₂ ⊆ Out D₇×M₄(2)	112	8+	(D7xM4(2)):4C2	448,1230
(D₇×M₄(2))⋊₅C₂ = D₇×C₄.D₄	φ: C₂/C₁ → C₂ ⊆ Out D₇×M₄(2)	56	8+	(D7xM4(2)):5C2	448,278
(D₇×M₄(2))⋊₆C₂ = M₄(2).₁₉D₁₄	φ: C₂/C₁ → C₂ ⊆ Out D₇×M₄(2)	112	8-	(D7xM4(2)):6C2	448,279
(D₇×M₄(2))⋊₇C₂ = M₄(2).₂₁D₁₄	φ: C₂/C₁ → C₂ ⊆ Out D₇×M₄(2)	112	8+	(D7xM4(2)):7C2	448,285
(D₇×M₄(2))⋊₈C₂ = D₇×C₄≀C₂	φ: C₂/C₁ → C₂ ⊆ Out D₇×M₄(2)	56	4	(D7xM4(2)):8C2	448,354
(D₇×M₄(2))⋊₉C₂ = C₄²⋊D₁₄	φ: C₂/C₁ → C₂ ⊆ Out D₇×M₄(2)	112	4	(D7xM4(2)):9C2	448,355
(D₇×M₄(2))⋊₁₀C₂ = C₂₈.₇₀C₂⁴	φ: C₂/C₁ → C₂ ⊆ Out D₇×M₄(2)	112	4	(D7xM4(2)):10C2	448,1198
(D₇×M₄(2))⋊₁₁C₂ = C₅₆.₄₉C₂³	φ: C₂/C₁ → C₂ ⊆ Out D₇×M₄(2)	112	4	(D7xM4(2)):11C2	448,1203
(D₇×M₄(2))⋊₁₂C₂ = D₇×C₈○D₄	φ: trivial image	112	4	(D7xM4(2)):12C2	448,1202

Non-split extensions G=N.Q with N=D₇×M₄(2) and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
(D₇×M₄(2)).₁C₂ = D₇×C₄.₁₀D₄	φ: C₂/C₁ → C₂ ⊆ Out D₇×M₄(2)	112	8-	(D7xM4(2)).1C2	448,284
(D₇×M₄(2)).₂C₂ = D₇×C₈.C₄	φ: C₂/C₁ → C₂ ⊆ Out D₇×M₄(2)	112	4	(D7xM4(2)).2C2	448,426
(D₇×M₄(2)).₃C₂ = M₄(2).₂₅D₁₄	φ: C₂/C₁ → C₂ ⊆ Out D₇×M₄(2)	112	4	(D7xM4(2)).3C2	448,427

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