Extensions 1→N→G→Q→1 with N=D₄ and Q=C₃²⋊C₄

Direct product G=N×Q with N=D₄ and Q=C₃²⋊C₄

		d	ρ	Label	ID
D₄×C₃²⋊C₄		24	8+	D4xC3^2:C4	288,936

Semidirect products G=N:Q with N=D₄ and Q=C₃²⋊C₄

extension	φ:Q→Out N	d	ρ	Label	ID
D₄⋊₁(C₃²⋊C₄) = C₃⋊S₃.₅D₈	φ: C₃²⋊C₄/C₃⋊S₃ → C₂ ⊆ Out D₄	24	8+	D4:1(C3^2:C4)	288,430
D₄⋊₂(C₃²⋊C₄) = C₃²⋊₆C₄≀C₂	φ: C₃²⋊C₄/C₃⋊S₃ → C₂ ⊆ Out D₄	48	8-	D4:2(C3^2:C4)	288,431

Non-split extensions G=N.Q with N=D₄ and Q=C₃²⋊C₄

extension	φ:Q→Out N	d	ρ	Label	ID
D₄.(C₃²⋊C₄) = C₆².(C₂×C₄)	φ: trivial image	48	8-	D4.(C3^2:C4)	288,935

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=D4 and Q=C32⋊C4