Extensions 1→N→G→Q→1 with N=D₄ and Q=F₇

Direct product G=N×Q with N=D₄ and Q=F₇

		d	ρ	Label	ID
D₄×F₇		28	12+	D4xF7	336,125

Semidirect products G=N:Q with N=D₄ and Q=F₇

extension	φ:Q→Out N	d	ρ	Label	ID
D₄⋊F₇ = D₄⋊F₇	φ: F₇/C₇⋊C₃ → C₂ ⊆ Out D₄	56	12+	D4:F7	336,18
D₄⋊₂F₇ = D₄⋊₂F₇	φ: trivial image	56	12-	D4:2F7	336,126

Non-split extensions G=N.Q with N=D₄ and Q=F₇

extension	φ:Q→Out N	d	ρ	Label	ID
D₄.F₇ = D₄.F₇	φ: F₇/C₇⋊C₃ → C₂ ⊆ Out D₄	56	12-	D4.F7	336,19

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=D4 and Q=F7