Extensions 1→N→G→Q→1 with N=Q₈⋊₃D₁₅ and Q=C₂

Direct product G=N×Q with N=Q₈⋊₃D₁₅ and Q=C₂

		d	ρ	Label	ID
C₂×Q₈⋊₃D₁₅		240		C2xQ8:3D15	480,1173

Semidirect products G=N:Q with N=Q₈⋊₃D₁₅ and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
Q₈⋊₃D₁₅⋊₁C₂ = D₆₀⋊C₂²	φ: C₂/C₁ → C₂ ⊆ Out Q₈⋊₃D₁₅	120	8+	Q8:3D15:1C2	480,582
Q₈⋊₃D₁₅⋊₂C₂ = D₂₀.₁₆D₆	φ: C₂/C₁ → C₂ ⊆ Out Q₈⋊₃D₁₅	240	8+	Q8:3D15:2C2	480,597
Q₈⋊₃D₁₅⋊₃C₂ = D₁₂.D₁₀	φ: C₂/C₁ → C₂ ⊆ Out Q₈⋊₃D₁₅	240	8+	Q8:3D15:3C2	480,599
Q₈⋊₃D₁₅⋊₄C₂ = C₃₀.₃₃C₂⁴	φ: C₂/C₁ → C₂ ⊆ Out Q₈⋊₃D₁₅	240	8+	Q8:3D15:4C2	480,1105
Q₈⋊₃D₁₅⋊₅C₂ = D₅×Q₈⋊₃S₃	φ: C₂/C₁ → C₂ ⊆ Out Q₈⋊₃D₁₅	120	8+	Q8:3D15:5C2	480,1108
Q₈⋊₃D₁₅⋊₆C₂ = S₃×Q₈⋊₂D₅	φ: C₂/C₁ → C₂ ⊆ Out Q₈⋊₃D₁₅	120	8+	Q8:3D15:6C2	480,1109
Q₈⋊₃D₁₅⋊₇C₂ = D₂₀⋊₁₇D₆	φ: C₂/C₁ → C₂ ⊆ Out Q₈⋊₃D₁₅	120	8+	Q8:3D15:7C2	480,1111
Q₈⋊₃D₁₅⋊₈C₂ = Q₈⋊₃D₃₀	φ: C₂/C₁ → C₂ ⊆ Out Q₈⋊₃D₁₅	120	4+	Q8:3D15:8C2	480,879
Q₈⋊₃D₁₅⋊₉C₂ = D₄.₅D₃₀	φ: C₂/C₁ → C₂ ⊆ Out Q₈⋊₃D₁₅	240	4	Q8:3D15:9C2	480,881
Q₈⋊₃D₁₅⋊₁₀C₂ = D₁₂₀⋊₈C₂	φ: C₂/C₁ → C₂ ⊆ Out Q₈⋊₃D₁₅	240	4+	Q8:3D15:10C2	480,884
Q₈⋊₃D₁₅⋊₁₁C₂ = Q₈.₁₅D₃₀	φ: C₂/C₁ → C₂ ⊆ Out Q₈⋊₃D₁₅	240	4	Q8:3D15:11C2	480,1174
Q₈⋊₃D₁₅⋊₁₂C₂ = D₄⋊₈D₃₀	φ: C₂/C₁ → C₂ ⊆ Out Q₈⋊₃D₁₅	120	4+	Q8:3D15:12C2	480,1176
Q₈⋊₃D₁₅⋊₁₃C₂ = C₄○D₄×D₁₅	φ: trivial image	120	4	Q8:3D15:13C2	480,1175

Non-split extensions G=N.Q with N=Q₈⋊₃D₁₅ and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
Q₈⋊₃D₁₅.₁C₂ = C₆₀.C₂³	φ: C₂/C₁ → C₂ ⊆ Out Q₈⋊₃D₁₅	240	8+	Q8:3D15.1C2	480,588
Q₈⋊₃D₁₅.₂C₂ = Q₁₆⋊D₁₅	φ: C₂/C₁ → C₂ ⊆ Out Q₈⋊₃D₁₅	240	4	Q8:3D15.2C2	480,883

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁