Extensions 1→N→G→Q→1 with N=D₄ and Q=C₃²×C₆

Direct product G=N×Q with N=D₄ and Q=C₃²×C₆

		d	ρ	Label	ID
D₄×C₃²×C₆		216		D4xC3^2xC6	432,731

Semidirect products G=N:Q with N=D₄ and Q=C₃²×C₆

extension	φ:Q→Out N	d	ρ	Label	ID
D₄⋊(C₃²×C₆) = D₈×C₃³	φ: C₃²×C₆/C₃³ → C₂ ⊆ Out D₄	216		D4:(C3^2xC6)	432,517
D₄⋊₂(C₃²×C₆) = C₄○D₄×C₃³	φ: trivial image	216		D4:2(C3^2xC6)	432,733

Non-split extensions G=N.Q with N=D₄ and Q=C₃²×C₆

extension	φ:Q→Out N	d	ρ	Label	ID
D₄.(C₃²×C₆) = SD₁₆×C₃³	φ: C₃²×C₆/C₃³ → C₂ ⊆ Out D₄	216		D4.(C3^2xC6)	432,518

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=D4 and Q=C32×C6