Extensions 1→N→G→Q→1 with N=D₄ and Q=C₄₂

Direct product G=N×Q with N=D₄ and Q=C₄₂

		d	ρ	Label	ID
D₄×C₄₂		168		D4xC42	336,205

Semidirect products G=N:Q with N=D₄ and Q=C₄₂

extension	φ:Q→Out N	d	ρ	Label	ID
D₄⋊C₄₂ = D₈×C₂₁	φ: C₄₂/C₂₁ → C₂ ⊆ Out D₄	168	2	D4:C42	336,111
D₄⋊₂C₄₂ = C₄○D₄×C₂₁	φ: trivial image	168	2	D4:2C42	336,207

Non-split extensions G=N.Q with N=D₄ and Q=C₄₂

extension	φ:Q→Out N	d	ρ	Label	ID
D₄.C₄₂ = SD₁₆×C₂₁	φ: C₄₂/C₂₁ → C₂ ⊆ Out D₄	168	2	D4.C42	336,112

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=D4 and Q=C42