Extensions 1→N→G→Q→1 with N=Q₈ and Q=C₂×C₂₂

Direct product G=N×Q with N=Q₈ and Q=C₂×C₂₂

		d	ρ	Label	ID
Q₈×C₂×C₂₂		352		Q8xC2xC22	352,190

Semidirect products G=N:Q with N=Q₈ and Q=C₂×C₂₂

extension	φ:Q→Out N	d	ρ	Label	ID
Q₈⋊₁(C₂×C₂₂) = SD₁₆×C₂₂	φ: C₂×C₂₂/C₂₂ → C₂ ⊆ Out Q₈	176		Q8:1(C2xC22)	352,168
Q₈⋊₂(C₂×C₂₂) = C₁₁×C₈⋊C₂²	φ: C₂×C₂₂/C₂₂ → C₂ ⊆ Out Q₈	88	4	Q8:2(C2xC22)	352,171
Q₈⋊₃(C₂×C₂₂) = C₄○D₄×C₂₂	φ: trivial image	176		Q8:3(C2xC22)	352,191
Q₈⋊₄(C₂×C₂₂) = C₁₁×2₊¹⁺⁴	φ: trivial image	88	4	Q8:4(C2xC22)	352,192

Non-split extensions G=N.Q with N=Q₈ and Q=C₂×C₂₂

extension	φ:Q→Out N	d	ρ	Label	ID
Q₈.₁(C₂×C₂₂) = Q₁₆×C₂₂	φ: C₂×C₂₂/C₂₂ → C₂ ⊆ Out Q₈	352		Q8.1(C2xC22)	352,169
Q₈.₂(C₂×C₂₂) = C₁₁×C₄○D₈	φ: C₂×C₂₂/C₂₂ → C₂ ⊆ Out Q₈	176	2	Q8.2(C2xC22)	352,170
Q₈.₃(C₂×C₂₂) = C₁₁×C₈.C₂²	φ: C₂×C₂₂/C₂₂ → C₂ ⊆ Out Q₈	176	4	Q8.3(C2xC22)	352,172
Q₈.₄(C₂×C₂₂) = C₁₁×2_-¹⁺⁴	φ: trivial image	176	4	Q8.4(C2xC22)	352,193

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁