Extensions 1→N→G→Q→1 with N=C₇ and Q=C₈⋊C₂²

Direct product G=N×Q with N=C₇ and Q=C₈⋊C₂²

		d	ρ	Label	ID
C₇×C₈⋊C₂²		56	4	C7xC8:C2^2	224,171

Semidirect products G=N:Q with N=C₇ and Q=C₈⋊C₂²

extension	φ:Q→Aut N	d	ρ	Label	ID
C₇⋊₁(C₈⋊C₂²) = C₈⋊D₁₄	φ: C₈⋊C₂²/M₄(2) → C₂ ⊆ Aut C₇	56	4+	C7:1(C8:C2^2)	224,103
C₇⋊₂(C₈⋊C₂²) = D₈⋊D₇	φ: C₈⋊C₂²/D₈ → C₂ ⊆ Aut C₇	56	4	C7:2(C8:C2^2)	224,106
C₇⋊₃(C₈⋊C₂²) = D₅₆⋊C₂	φ: C₈⋊C₂²/SD₁₆ → C₂ ⊆ Aut C₇	56	4+	C7:3(C8:C2^2)	224,109
C₇⋊₄(C₈⋊C₂²) = D₄.D₁₄	φ: C₈⋊C₂²/C₂×D₄ → C₂ ⊆ Aut C₇	56	4	C7:4(C8:C2^2)	224,127
C₇⋊₅(C₈⋊C₂²) = D₄⋊D₁₄	φ: C₈⋊C₂²/C₄○D₄ → C₂ ⊆ Aut C₇	56	4+	C7:5(C8:C2^2)	224,144

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