Extensions 1→N→G→Q→1 with N=D₄ and Q=S₄

Direct product G=N×Q with N=D₄ and Q=S₄

		d	ρ	Label	ID
D₄×S₄		12	6+	D4xS4	192,1472

Semidirect products G=N:Q with N=D₄ and Q=S₄

extension	φ:Q→Out N	d	ρ	Label	ID
D₄⋊S₄ = D₄⋊S₄	φ: S₄/A₄ → C₂ ⊆ Out D₄	24	6+	D4:S4	192,974
D₄⋊₂S₄ = D₄⋊₂S₄	φ: trivial image	24	6	D4:2S4	192,1473

Non-split extensions G=N.Q with N=D₄ and Q=S₄

extension	φ:Q→Out N	d	ρ	Label	ID
D₄.₁S₄ = A₄⋊SD₁₆	φ: S₄/A₄ → C₂ ⊆ Out D₄	24	6	D4.1S4	192,973
D₄.₂S₄ = D₄.S₄	φ: S₄/A₄ → C₂ ⊆ Out D₄	32	4-	D4.2S4	192,989
D₄.₃S₄ = D₄.₃S₄	φ: S₄/A₄ → C₂ ⊆ Out D₄	32	4	D4.3S4	192,990
D₄.₄S₄ = D₄.₄S₄	φ: trivial image	16	4	D4.4S4	192,1485
D₄.₅S₄ = D₄.₅S₄	φ: trivial image	32	4-	D4.5S4	192,1486

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