Extensions 1→N→G→Q→1 with N=C₄ and Q=C₇×M₄(2)

Direct product G=N×Q with N=C₄ and Q=C₇×M₄(2)

		d	ρ	Label	ID
M₄(2)×C₂₈		224		M4(2)xC28	448,812

Semidirect products G=N:Q with N=C₄ and Q=C₇×M₄(2)

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄⋊₁(C₇×M₄(2)) = C₇×C₈⋊₆D₄	φ: C₇×M₄(2)/C₅₆ → C₂ ⊆ Aut C₄	224		C4:1(C7xM4(2))	448,844
C₄⋊₂(C₇×M₄(2)) = C₇×C₄⋊M₄(2)	φ: C₇×M₄(2)/C₂×C₂₈ → C₂ ⊆ Aut C₄	224		C4:2(C7xM4(2))	448,831

Non-split extensions G=N.Q with N=C₄ and Q=C₇×M₄(2)

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄.₁(C₇×M₄(2)) = C₇×D₄⋊C₈	φ: C₇×M₄(2)/C₅₆ → C₂ ⊆ Aut C₄	224		C4.1(C7xM4(2))	448,129
C₄.₂(C₇×M₄(2)) = C₇×Q₈⋊C₈	φ: C₇×M₄(2)/C₅₆ → C₂ ⊆ Aut C₄	448		C4.2(C7xM4(2))	448,130
C₄.₃(C₇×M₄(2)) = C₇×C₈⋊₄Q₈	φ: C₇×M₄(2)/C₅₆ → C₂ ⊆ Aut C₄	448		C4.3(C7xM4(2))	448,854
C₄.₄(C₇×M₄(2)) = C₇×C₈⋊₂C₈	φ: C₇×M₄(2)/C₂×C₂₈ → C₂ ⊆ Aut C₄	448		C4.4(C7xM4(2))	448,138
C₄.₅(C₇×M₄(2)) = C₇×C₈⋊₁C₈	φ: C₇×M₄(2)/C₂×C₂₈ → C₂ ⊆ Aut C₄	448		C4.5(C7xM4(2))	448,139
C₄.₆(C₇×M₄(2)) = C₇×C₁₆⋊C₄	φ: C₇×M₄(2)/C₂×C₂₈ → C₂ ⊆ Aut C₄	112	4	C4.6(C7xM4(2))	448,151
C₄.₇(C₇×M₄(2)) = C₇×C₂³.C₈	φ: C₇×M₄(2)/C₂×C₂₈ → C₂ ⊆ Aut C₄	112	4	C4.7(C7xM4(2))	448,153
C₄.₈(C₇×M₄(2)) = C₇×C₄².₆C₄	φ: C₇×M₄(2)/C₂×C₂₈ → C₂ ⊆ Aut C₄	224		C4.8(C7xM4(2))	448,840
C₄.₉(C₇×M₄(2)) = C₇×C₈⋊C₈	central extension (φ=1)	448		C4.9(C7xM4(2))	448,126
C₄.₁₀(C₇×M₄(2)) = C₇×C₂²⋊C₁₆	central extension (φ=1)	224		C4.10(C7xM4(2))	448,152
C₄.₁₁(C₇×M₄(2)) = C₇×C₄⋊C₁₆	central extension (φ=1)	448		C4.11(C7xM4(2))	448,167
C₄.₁₂(C₇×M₄(2)) = C₇×C₄².₁₂C₄	central extension (φ=1)	224		C4.12(C7xM4(2))	448,839

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