Extensions 1→N→G→Q→1 with N=C₂² and Q=C₇×M₄(2)

Direct product G=N×Q with N=C₂² and Q=C₇×M₄(2)

		d	ρ	Label	ID
M₄(2)×C₂×C₁₄		224		M4(2)xC2xC14	448,1349

Semidirect products G=N:Q with N=C₂² and Q=C₇×M₄(2)

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂²⋊₁(C₇×M₄(2)) = C₇×C₈⋊₉D₄	φ: C₇×M₄(2)/C₅₆ → C₂ ⊆ Aut C₂²	224		C2^2:1(C7xM4(2))	448,843
C₂²⋊₂(C₇×M₄(2)) = C₇×C₂⁴.₄C₄	φ: C₇×M₄(2)/C₂×C₂₈ → C₂ ⊆ Aut C₂²	112		C2^2:2(C7xM4(2))	448,815

Non-split extensions G=N.Q with N=C₂² and Q=C₇×M₄(2)

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂².₁(C₇×M₄(2)) = C₇×D₄.C₈	φ: C₇×M₄(2)/C₅₆ → C₂ ⊆ Aut C₂²	224	2	C2^2.1(C7xM4(2))	448,154
C₂².₂(C₇×M₄(2)) = C₇×C₂³⋊C₈	φ: C₇×M₄(2)/C₂×C₂₈ → C₂ ⊆ Aut C₂²	112		C2^2.2(C7xM4(2))	448,127
C₂².₃(C₇×M₄(2)) = C₇×C₂².M₄(2)	φ: C₇×M₄(2)/C₂×C₂₈ → C₂ ⊆ Aut C₂²	224		C2^2.3(C7xM4(2))	448,128
C₂².₄(C₇×M₄(2)) = C₇×C₁₆⋊C₄	φ: C₇×M₄(2)/C₂×C₂₈ → C₂ ⊆ Aut C₂²	112	4	C2^2.4(C7xM4(2))	448,151
C₂².₅(C₇×M₄(2)) = C₇×C₈.C₈	φ: C₇×M₄(2)/C₂×C₂₈ → C₂ ⊆ Aut C₂²	112	2	C2^2.5(C7xM4(2))	448,168
C₂².₆(C₇×M₄(2)) = C₇×C₄².₆C₄	φ: C₇×M₄(2)/C₂×C₂₈ → C₂ ⊆ Aut C₂²	224		C2^2.6(C7xM4(2))	448,840
C₂².₇(C₇×M₄(2)) = C₇×C₂².₇C₄²	central extension (φ=1)	448		C2^2.7(C7xM4(2))	448,140
C₂².₈(C₇×M₄(2)) = C₁₄×C₈⋊C₄	central extension (φ=1)	448		C2^2.8(C7xM4(2))	448,811
C₂².₉(C₇×M₄(2)) = C₁₄×C₂²⋊C₈	central extension (φ=1)	224		C2^2.9(C7xM4(2))	448,814
C₂².₁₀(C₇×M₄(2)) = C₁₄×C₄⋊C₈	central extension (φ=1)	448		C2^2.10(C7xM4(2))	448,830

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