Extensions 1→N→G→Q→1 with N=Q₈ and Q=C₆

Direct product G=N×Q with N=Q₈ and Q=C₆

		d	ρ	Label	ID
C₆×Q₈		48		C6xQ8	48,46

Semidirect products G=N:Q with N=Q₈ and Q=C₆

extension	φ:Q→Out N	d	ρ	Label	ID
Q₈⋊C₆ = C₂×SL₂(𝔽₃)	φ: C₆/C₂ → C₃ ⊆ Out Q₈	16		Q8:C6	48,32
Q₈⋊₂C₆ = C₃×SD₁₆	φ: C₆/C₃ → C₂ ⊆ Out Q₈	24	2	Q8:2C6	48,26
Q₈⋊₃C₆ = C₃×C₄○D₄	φ: trivial image	24	2	Q8:3C6	48,47

Non-split extensions G=N.Q with N=Q₈ and Q=C₆

extension	φ:Q→Out N	d	ρ	Label	ID
Q₈.C₆ = C₄.A₄	φ: C₆/C₂ → C₃ ⊆ Out Q₈	16	2	Q8.C6	48,33
Q₈.₂C₆ = C₃×Q₁₆	φ: C₆/C₃ → C₂ ⊆ Out Q₈	48	2	Q8.2C6	48,27

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=Q8 and Q=C6