Extensions 1→N→G→Q→1 with N=Q₈ and Q=S₃

Direct product G=N×Q with N=Q₈ and Q=S₃

		d	ρ	Label	ID
S₃×Q₈		24	4-	S3xQ8	48,40

Semidirect products G=N:Q with N=Q₈ and Q=S₃

extension	φ:Q→Out N	d	ρ	Label	ID
Q₈⋊S₃ = GL₂(𝔽₃)	φ: S₃/C₁ → S₃ ⊆ Out Q₈	8	2	Q8:S3	48,29
Q₈⋊₂S₃ = Q₈⋊₂S₃	φ: S₃/C₃ → C₂ ⊆ Out Q₈	24	4+	Q8:2S3	48,17
Q₈⋊₃S₃ = Q₈⋊₃S₃	φ: trivial image	24	4+	Q8:3S3	48,41

Non-split extensions G=N.Q with N=Q₈ and Q=S₃

extension	φ:Q→Out N	d	ρ	Label	ID
Q₈.S₃ = CSU₂(𝔽₃)	φ: S₃/C₁ → S₃ ⊆ Out Q₈	16	2-	Q8.S3	48,28
Q₈.₂S₃ = C₃⋊Q₁₆	φ: S₃/C₃ → C₂ ⊆ Out Q₈	48	4-	Q8.2S3	48,18

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Extensions 1→N→G→Q→1 with N=Q8 and Q=S3