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

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

		d	ρ	Label	ID
S₃×Q₈×C₉		144	4	S3xQ8xC9	432,366

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

extension	φ:Q→Out N	d	ρ	Label	ID
Q₈⋊(S₃×C₉) = C₉×GL₂(𝔽₃)	φ: S₃×C₉/C₉ → S₃ ⊆ Out Q₈	72	2	Q8:(S3xC9)	432,241
Q₈⋊₂(S₃×C₉) = S₃×Q₈⋊C₉	φ: S₃×C₉/C₃×S₃ → C₃ ⊆ Out Q₈	144	4	Q8:2(S3xC9)	432,268
Q₈⋊₃(S₃×C₉) = C₉×Q₈⋊₂S₃	φ: S₃×C₉/C₃×C₉ → C₂ ⊆ Out Q₈	144	4	Q8:3(S3xC9)	432,158
Q₈⋊₄(S₃×C₉) = C₉×Q₈⋊₃S₃	φ: trivial image	144	4	Q8:4(S3xC9)	432,367

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

extension	φ:Q→Out N	d	ρ	Label	ID
Q₈.(S₃×C₉) = C₉×CSU₂(𝔽₃)	φ: S₃×C₉/C₉ → S₃ ⊆ Out Q₈	144	2	Q8.(S3xC9)	432,240
Q₈.₂(S₃×C₉) = Q₈⋊C₉⋊₃S₃	φ: S₃×C₉/C₃×S₃ → C₃ ⊆ Out Q₈	144	4	Q8.2(S3xC9)	432,267
Q₈.₃(S₃×C₉) = C₉×C₃⋊Q₁₆	φ: S₃×C₉/C₃×C₉ → C₂ ⊆ Out Q₈	144	4	Q8.3(S3xC9)	432,159

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