Extensions 1→N→G→Q→1 with N=D₄ and Q=C₂×Dic₇

Direct product G=N×Q with N=D₄ and Q=C₂×Dic₇

		d	ρ	Label	ID
C₂×D₄×Dic₇		224		C2xD4xDic7	448,1248

Semidirect products G=N:Q with N=D₄ and Q=C₂×Dic₇

extension	φ:Q→Out N	d	ρ	Label	ID
D₄⋊₁(C₂×Dic₇) = D₈×Dic₇	φ: C₂×Dic₇/Dic₇ → C₂ ⊆ Out D₄	224		D4:1(C2xDic7)	448,683
D₄⋊₂(C₂×Dic₇) = D₈⋊Dic₇	φ: C₂×Dic₇/Dic₇ → C₂ ⊆ Out D₄	224		D4:2(C2xDic7)	448,686
D₄⋊₃(C₂×Dic₇) = C₂×D₄⋊Dic₇	φ: C₂×Dic₇/C₂×C₁₄ → C₂ ⊆ Out D₄	224		D4:3(C2xDic7)	448,748
D₄⋊₄(C₂×Dic₇) = C₄○D₄⋊Dic₇	φ: C₂×Dic₇/C₂×C₁₄ → C₂ ⊆ Out D₄	224		D4:4(C2xDic7)	448,766
D₄⋊₅(C₂×Dic₇) = C₂×D₄⋊₂Dic₇	φ: C₂×Dic₇/C₂×C₁₄ → C₂ ⊆ Out D₄	112		D4:5(C2xDic7)	448,769
D₄⋊₆(C₂×Dic₇) = C₂⁴.₃₈D₁₄	φ: trivial image	112		D4:6(C2xDic7)	448,1251
D₄⋊₇(C₂×Dic₇) = C₄○D₄×Dic₇	φ: trivial image	224		D4:7(C2xDic7)	448,1279
D₄⋊₈(C₂×Dic₇) = C₁₄.₁₀₆2_-¹⁺⁴	φ: trivial image	224		D4:8(C2xDic7)	448,1280

Non-split extensions G=N.Q with N=D₄ and Q=C₂×Dic₇

extension	φ:Q→Out N	d	ρ	Label	ID
D₄.₁(C₂×Dic₇) = SD₁₆×Dic₇	φ: C₂×Dic₇/Dic₇ → C₂ ⊆ Out D₄	224		D4.1(C2xDic7)	448,695
D₄.₂(C₂×Dic₇) = SD₁₆⋊Dic₇	φ: C₂×Dic₇/Dic₇ → C₂ ⊆ Out D₄	224		D4.2(C2xDic7)	448,698
D₄.₃(C₂×Dic₇) = D₈⋊₅Dic₇	φ: C₂×Dic₇/Dic₇ → C₂ ⊆ Out D₄	112	4	D4.3(C2xDic7)	448,730
D₄.₄(C₂×Dic₇) = D₈⋊₄Dic₇	φ: C₂×Dic₇/Dic₇ → C₂ ⊆ Out D₄	112	4	D4.4(C2xDic7)	448,731
D₄.₅(C₂×Dic₇) = (D₄×C₁₄)⋊₆C₄	φ: C₂×Dic₇/C₂×C₁₄ → C₂ ⊆ Out D₄	112		D4.5(C2xDic7)	448,749
D₄.₆(C₂×Dic₇) = C₂₈.(C₂×D₄)	φ: C₂×Dic₇/C₂×C₁₄ → C₂ ⊆ Out D₄	224		D4.6(C2xDic7)	448,767
D₄.₇(C₂×Dic₇) = (D₄×C₁₄)⋊₉C₄	φ: C₂×Dic₇/C₂×C₁₄ → C₂ ⊆ Out D₄	112	4	D4.7(C2xDic7)	448,770
D₄.₈(C₂×Dic₇) = C₂×Q₈.Dic₇	φ: trivial image	224		D4.8(C2xDic7)	448,1271
D₄.₉(C₂×Dic₇) = C₂₈.₇₆C₂⁴	φ: trivial image	112	4	D4.9(C2xDic7)	448,1272

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