Extensions 1→N→G→Q→1 with N=Q₈×3_-¹⁺² and Q=C₂

Direct product G=N×Q with N=Q₈×3_-¹⁺² and Q=C₂

		d	ρ	Label	ID
C₂×Q₈×3_-¹⁺²		144		C2xQ8xES-(3,1)	432,408

Semidirect products G=N:Q with N=Q₈×3_-¹⁺² and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
(Q₈×3_-¹⁺²)⋊₁C₂ = D₃₆.C₆	φ: C₂/C₁ → C₂ ⊆ Out Q₈×3_-¹⁺²	72	12+	(Q8xES-(3,1)):1C2	432,163
(Q₈×3_-¹⁺²)⋊₂C₂ = Q₈×C₉⋊C₆	φ: C₂/C₁ → C₂ ⊆ Out Q₈×3_-¹⁺²	72	12-	(Q8xES-(3,1)):2C2	432,370
(Q₈×3_-¹⁺²)⋊₃C₂ = D₃₆⋊₃C₆	φ: C₂/C₁ → C₂ ⊆ Out Q₈×3_-¹⁺²	72	12+	(Q8xES-(3,1)):3C2	432,371
(Q₈×3_-¹⁺²)⋊₄C₂ = SD₁₆×3_-¹⁺²	φ: C₂/C₁ → C₂ ⊆ Out Q₈×3_-¹⁺²	72	6	(Q8xES-(3,1)):4C2	432,220
(Q₈×3_-¹⁺²)⋊₅C₂ = C₄○D₄×3_-¹⁺²	φ: trivial image	72	6	(Q8xES-(3,1)):5C2	432,411

Non-split extensions G=N.Q with N=Q₈×3_-¹⁺² and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
(Q₈×3_-¹⁺²).₁C₂ = Dic₁₈.C₆	φ: C₂/C₁ → C₂ ⊆ Out Q₈×3_-¹⁺²	144	12-	(Q8xES-(3,1)).1C2	432,162
(Q₈×3_-¹⁺²).₂C₂ = Q₁₆×3_-¹⁺²	φ: C₂/C₁ → C₂ ⊆ Out Q₈×3_-¹⁺²	144	6	(Q8xES-(3,1)).2C2	432,223

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁