Extensions 1→N→G→Q→1 with N=D₄ and Q=D₂₂

Direct product G=N×Q with N=D₄ and Q=D₂₂

		d	ρ	Label	ID
C₂×D₄×D₁₁		88		C2xD4xD11	352,177

Semidirect products G=N:Q with N=D₄ and Q=D₂₂

extension	φ:Q→Out N	d	ρ	Label	ID
D₄⋊₁D₂₂ = D₈×D₁₁	φ: D₂₂/D₁₁ → C₂ ⊆ Out D₄	88	4+	D4:1D22	352,105
D₄⋊₂D₂₂ = D₄⋊D₂₂	φ: D₂₂/D₁₁ → C₂ ⊆ Out D₄	88	4	D4:2D22	352,106
D₄⋊₃D₂₂ = C₂×D₄⋊D₁₁	φ: D₂₂/C₂₂ → C₂ ⊆ Out D₄	176		D4:3D22	352,126
D₄⋊₄D₂₂ = Q₈⋊D₂₂	φ: D₂₂/C₂₂ → C₂ ⊆ Out D₄	88	4+	D4:4D22	352,144
D₄⋊₅D₂₂ = C₂×D₄⋊₂D₁₁	φ: trivial image	176		D4:5D22	352,178
D₄⋊₆D₂₂ = D₄⋊₆D₂₂	φ: trivial image	88	4	D4:6D22	352,179
D₄⋊₇D₂₂ = C₄○D₄×D₁₁	φ: trivial image	88	4	D4:7D22	352,183
D₄⋊₈D₂₂ = D₄⋊₈D₂₂	φ: trivial image	88	4+	D4:8D22	352,184

Non-split extensions G=N.Q with N=D₄ and Q=D₂₂

extension	φ:Q→Out N	d	ρ	Label	ID
D₄.₁D₂₂ = D₈⋊₃D₁₁	φ: D₂₂/D₁₁ → C₂ ⊆ Out D₄	176	4-	D4.1D22	352,107
D₄.₂D₂₂ = SD₁₆×D₁₁	φ: D₂₂/D₁₁ → C₂ ⊆ Out D₄	88	4	D4.2D22	352,108
D₄.₃D₂₂ = D₈₈⋊C₂	φ: D₂₂/D₁₁ → C₂ ⊆ Out D₄	88	4+	D4.3D22	352,109
D₄.₄D₂₂ = D₄.D₂₂	φ: D₂₂/D₁₁ → C₂ ⊆ Out D₄	176	4-	D4.4D22	352,110
D₄.₅D₂₂ = Q₈.D₂₂	φ: D₂₂/D₁₁ → C₂ ⊆ Out D₄	176	4	D4.5D22	352,111
D₄.₆D₂₂ = D₄₄⋊₆C₂²	φ: D₂₂/C₂₂ → C₂ ⊆ Out D₄	88	4	D4.6D22	352,127
D₄.₇D₂₂ = C₂×D₄.D₁₁	φ: D₂₂/C₂₂ → C₂ ⊆ Out D₄	176		D4.7D22	352,128
D₄.₈D₂₂ = D₄.₈D₂₂	φ: D₂₂/C₂₂ → C₂ ⊆ Out D₄	176	4	D4.8D22	352,145
D₄.₉D₂₂ = D₄.₉D₂₂	φ: D₂₂/C₂₂ → C₂ ⊆ Out D₄	176	4-	D4.9D22	352,146
D₄.₁₀D₂₂ = D₄.₁₀D₂₂	φ: trivial image	176	4-	D4.10D22	352,185

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁