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

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

		d	ρ	Label	ID
C₂²×Q₈		32		C2^2xQ8	32,47

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

extension	φ:Q→Out N	d	ρ	Label	ID
Q₈⋊₁C₂² = C₂×SD₁₆	φ: C₂²/C₂ → C₂ ⊆ Out Q₈	16		Q8:1C2^2	32,40
Q₈⋊₂C₂² = C₈⋊C₂²	φ: C₂²/C₂ → C₂ ⊆ Out Q₈	8	4+	Q8:2C2^2	32,43
Q₈⋊₃C₂² = C₂×C₄○D₄	φ: trivial image	16		Q8:3C2^2	32,48
Q₈⋊₄C₂² = 2₊¹⁺⁴	φ: trivial image	8	4+	Q8:4C2^2	32,49

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

extension	φ:Q→Out N	d	ρ	Label	ID
Q₈.₁C₂² = C₂×Q₁₆	φ: C₂²/C₂ → C₂ ⊆ Out Q₈	32		Q8.1C2^2	32,41
Q₈.₂C₂² = C₄○D₈	φ: C₂²/C₂ → C₂ ⊆ Out Q₈	16	2	Q8.2C2^2	32,42
Q₈.₃C₂² = C₈.C₂²	φ: C₂²/C₂ → C₂ ⊆ Out Q₈	16	4-	Q8.3C2^2	32,44
Q₈.₄C₂² = 2_-¹⁺⁴	φ: trivial image	16	4-	Q8.4C2^2	32,50

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁