Extensions 1→N→G→Q→1 with N=Q₈ and Q=C₉⋊S₃

Direct product G=N×Q with N=Q₈ and Q=C₉⋊S₃

		d	ρ	Label	ID
Q₈×C₉⋊S₃		216		Q8xC9:S3	432,392

Semidirect products G=N:Q with N=Q₈ and Q=C₉⋊S₃

extension	φ:Q→Out N	d	ρ	Label	ID
Q₈⋊₁(C₉⋊S₃) = C₁₈.₆S₄	φ: C₉⋊S₃/C₉ → S₃ ⊆ Out Q₈	72	4+	Q8:1(C9:S3)	432,253
Q₈⋊₂(C₉⋊S₃) = C₃².₃GL₂(𝔽₃)	φ: C₉⋊S₃/C₃² → S₃ ⊆ Out Q₈	216		Q8:2(C9:S3)	432,256
Q₈⋊₃(C₉⋊S₃) = C₃₆.₂₀D₆	φ: C₉⋊S₃/C₃×C₉ → C₂ ⊆ Out Q₈	216		Q8:3(C9:S3)	432,195
Q₈⋊₄(C₉⋊S₃) = C₃₆.₂₉D₆	φ: trivial image	216		Q8:4(C9:S3)	432,393

Non-split extensions G=N.Q with N=Q₈ and Q=C₉⋊S₃

extension	φ:Q→Out N	d	ρ	Label	ID
Q₈.₁(C₉⋊S₃) = C₁₈.₅S₄	φ: C₉⋊S₃/C₉ → S₃ ⊆ Out Q₈	144	4-	Q8.1(C9:S3)	432,252
Q₈.₂(C₉⋊S₃) = C₃².₃CSU₂(𝔽₃)	φ: C₉⋊S₃/C₃² → S₃ ⊆ Out Q₈	432		Q8.2(C9:S3)	432,255
Q₈.₃(C₉⋊S₃) = C₃₆.₁₉D₆	φ: C₉⋊S₃/C₃×C₉ → C₂ ⊆ Out Q₈	432		Q8.3(C9:S3)	432,194

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