Extensions 1→N→G→Q→1 with N=C₂³×C₄ and Q=D₇

Direct product G=N×Q with N=C₂³×C₄ and Q=D₇

		d	ρ	Label	ID
D₇×C₂³×C₄		224		D7xC2^3xC4	448,1366

Semidirect products G=N:Q with N=C₂³×C₄ and Q=D₇

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂³×C₄)⋊₁D₇ = C₂³.₂₈D₂₈	φ: D₇/C₇ → C₂ ⊆ Aut C₂³×C₄	224		(C2^3xC4):1D7	448,747
(C₂³×C₄)⋊₂D₇ = C₂²×D₁₄⋊C₄	φ: D₇/C₇ → C₂ ⊆ Aut C₂³×C₄	224		(C2^3xC4):2D7	448,1240
(C₂³×C₄)⋊₃D₇ = C₂×C₄×C₇⋊D₄	φ: D₇/C₇ → C₂ ⊆ Aut C₂³×C₄	224		(C2^3xC4):3D7	448,1241
(C₂³×C₄)⋊₄D₇ = C₂×C₂³.₂₃D₁₄	φ: D₇/C₇ → C₂ ⊆ Aut C₂³×C₄	224		(C2^3xC4):4D7	448,1242
(C₂³×C₄)⋊₅D₇ = C₂×C₂₈⋊₇D₄	φ: D₇/C₇ → C₂ ⊆ Aut C₂³×C₄	224		(C2^3xC4):5D7	448,1243
(C₂³×C₄)⋊₆D₇ = C₂⁴.₇₂D₁₄	φ: D₇/C₇ → C₂ ⊆ Aut C₂³×C₄	112		(C2^3xC4):6D7	448,1244
(C₂³×C₄)⋊₇D₇ = C₂³×D₂₈	φ: D₇/C₇ → C₂ ⊆ Aut C₂³×C₄	224		(C2^3xC4):7D7	448,1367
(C₂³×C₄)⋊₈D₇ = C₂²×C₄○D₂₈	φ: D₇/C₇ → C₂ ⊆ Aut C₂³×C₄	224		(C2^3xC4):8D7	448,1368

Non-split extensions G=N.Q with N=C₂³×C₄ and Q=D₇

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂³×C₄).₁D₇ = C₂×C₂₈.₅₅D₄	φ: D₇/C₇ → C₂ ⊆ Aut C₂³×C₄	224		(C2^3xC4).1D7	448,740
(C₂³×C₄).₂D₇ = C₂×C₁₄.C₄²	φ: D₇/C₇ → C₂ ⊆ Aut C₂³×C₄	448		(C2^3xC4).2D7	448,742
(C₂³×C₄).₃D₇ = C₄×C₂³.D₇	φ: D₇/C₇ → C₂ ⊆ Aut C₂³×C₄	224		(C2^3xC4).3D7	448,743
(C₂³×C₄).₄D₇ = C₂⁴.₆₂D₁₄	φ: D₇/C₇ → C₂ ⊆ Aut C₂³×C₄	224		(C2^3xC4).4D7	448,744
(C₂³×C₄).₅D₇ = C₂⁴.₆₃D₁₄	φ: D₇/C₇ → C₂ ⊆ Aut C₂³×C₄	224		(C2^3xC4).5D7	448,745
(C₂³×C₄).₆D₇ = C₂²×Dic₇⋊C₄	φ: D₇/C₇ → C₂ ⊆ Aut C₂³×C₄	448		(C2^3xC4).6D7	448,1236
(C₂³×C₄).₇D₇ = C₂⁴.₄Dic₇	φ: D₇/C₇ → C₂ ⊆ Aut C₂³×C₄	112		(C2^3xC4).7D7	448,741
(C₂³×C₄).₈D₇ = C₂³.₂₇D₂₈	φ: D₇/C₇ → C₂ ⊆ Aut C₂³×C₄	224		(C2^3xC4).8D7	448,746
(C₂³×C₄).₉D₇ = C₂²×C₄.Dic₇	φ: D₇/C₇ → C₂ ⊆ Aut C₂³×C₄	224		(C2^3xC4).9D7	448,1234
(C₂³×C₄).₁₀D₇ = C₂×C₂₈.₄₈D₄	φ: D₇/C₇ → C₂ ⊆ Aut C₂³×C₄	224		(C2^3xC4).10D7	448,1237
(C₂³×C₄).₁₁D₇ = C₂²×C₄⋊Dic₇	φ: D₇/C₇ → C₂ ⊆ Aut C₂³×C₄	448		(C2^3xC4).11D7	448,1238
(C₂³×C₄).₁₂D₇ = C₂×C₂³.₂₁D₁₄	φ: D₇/C₇ → C₂ ⊆ Aut C₂³×C₄	224		(C2^3xC4).12D7	448,1239
(C₂³×C₄).₁₃D₇ = C₂³×Dic₁₄	φ: D₇/C₇ → C₂ ⊆ Aut C₂³×C₄	448		(C2^3xC4).13D7	448,1365
(C₂³×C₄).₁₄D₇ = C₂³×C₇⋊C₈	central extension (φ=1)	448		(C2^3xC4).14D7	448,1233
(C₂³×C₄).₁₅D₇ = C₂²×C₄×Dic₇	central extension (φ=1)	448		(C2^3xC4).15D7	448,1235

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