Extensions 1→N→G→Q→1 with N=D₄ and Q=D₃₁

Direct product G=N×Q with N=D₄ and Q=D₃₁

		d	ρ	Label	ID
D₄×D₃₁		124	4+	D4xD31	496,31

Semidirect products G=N:Q with N=D₄ and Q=D₃₁

extension	φ:Q→Out N	d	ρ	Label	ID
D₄⋊D₃₁ = D₄⋊D₃₁	φ: D₃₁/C₃₁ → C₂ ⊆ Out D₄	248	4+	D4:D31	496,14
D₄⋊₂D₃₁ = D₄⋊₂D₃₁	φ: trivial image	248	4-	D4:2D31	496,32

Non-split extensions G=N.Q with N=D₄ and Q=D₃₁

extension	φ:Q→Out N	d	ρ	Label	ID
D₄.D₃₁ = D₄.D₃₁	φ: D₃₁/C₃₁ → C₂ ⊆ Out D₄	248	4-	D4.D31	496,15

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Extensions 1→N→G→Q→1 with N=D4 and Q=D31