Extensions 1→N→G→Q→1 with N=D₄ and Q=C₅₄

Direct product G=N×Q with N=D₄ and Q=C₅₄

		d	ρ	Label	ID
D₄×C₅₄		216		D4xC54	432,54

Semidirect products G=N:Q with N=D₄ and Q=C₅₄

extension	φ:Q→Out N	d	ρ	Label	ID
D₄⋊C₅₄ = D₈×C₂₇	φ: C₅₄/C₂₇ → C₂ ⊆ Out D₄	216	2	D4:C54	432,25
D₄⋊₂C₅₄ = C₄○D₄×C₂₇	φ: trivial image	216	2	D4:2C54	432,56

Non-split extensions G=N.Q with N=D₄ and Q=C₅₄

extension	φ:Q→Out N	d	ρ	Label	ID
D₄.C₅₄ = SD₁₆×C₂₇	φ: C₅₄/C₂₇ → C₂ ⊆ Out D₄	216	2	D4.C54	432,26

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Extensions 1→N→G→Q→1 with N=D4 and Q=C54