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

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

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

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

extension	φ:Q→Out N	d	ρ	Label	ID
(Q₈×C₉)⋊₁S₃ = C₁₈.₆S₄	φ: S₃/C₁ → S₃ ⊆ Out Q₈×C₉	72	4+	(Q8xC9):1S3	432,253
(Q₈×C₉)⋊₂S₃ = C₉×GL₂(𝔽₃)	φ: S₃/C₁ → S₃ ⊆ Out Q₈×C₉	72	2	(Q8xC9):2S3	432,241
(Q₈×C₉)⋊₃S₃ = C₃₆.₂₀D₆	φ: S₃/C₃ → C₂ ⊆ Out Q₈×C₉	216		(Q8xC9):3S3	432,195
(Q₈×C₉)⋊₄S₃ = Q₈×C₉⋊S₃	φ: S₃/C₃ → C₂ ⊆ Out Q₈×C₉	216		(Q8xC9):4S3	432,392
(Q₈×C₉)⋊₅S₃ = C₃₆.₂₉D₆	φ: S₃/C₃ → C₂ ⊆ Out Q₈×C₉	216		(Q8xC9):5S3	432,393
(Q₈×C₉)⋊₆S₃ = C₉×Q₈⋊₂S₃	φ: S₃/C₃ → C₂ ⊆ Out Q₈×C₉	144	4	(Q8xC9):6S3	432,158
(Q₈×C₉)⋊₇S₃ = C₉×Q₈⋊₃S₃	φ: trivial image	144	4	(Q8xC9):7S3	432,367

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

extension	φ:Q→Out N	d	ρ	Label	ID
(Q₈×C₉).₁S₃ = Q₈.D₂₇	φ: S₃/C₁ → S₃ ⊆ Out Q₈×C₉	432	4-	(Q8xC9).1S3	432,37
(Q₈×C₉).₂S₃ = Q₈⋊D₂₇	φ: S₃/C₁ → S₃ ⊆ Out Q₈×C₉	216	4+	(Q8xC9).2S3	432,38
(Q₈×C₉).₃S₃ = C₁₈.₅S₄	φ: S₃/C₁ → S₃ ⊆ Out Q₈×C₉	144	4-	(Q8xC9).3S3	432,252
(Q₈×C₉).₄S₃ = C₉×CSU₂(𝔽₃)	φ: S₃/C₁ → S₃ ⊆ Out Q₈×C₉	144	2	(Q8xC9).4S3	432,240
(Q₈×C₉).₅S₃ = C₂₇⋊Q₁₆	φ: S₃/C₃ → C₂ ⊆ Out Q₈×C₉	432	4-	(Q8xC9).5S3	432,17
(Q₈×C₉).₆S₃ = Q₈⋊₂D₂₇	φ: S₃/C₃ → C₂ ⊆ Out Q₈×C₉	216	4+	(Q8xC9).6S3	432,18
(Q₈×C₉).₇S₃ = Q₈×D₂₇	φ: S₃/C₃ → C₂ ⊆ Out Q₈×C₉	216	4-	(Q8xC9).7S3	432,49
(Q₈×C₉).₈S₃ = Q₈⋊₃D₂₇	φ: S₃/C₃ → C₂ ⊆ Out Q₈×C₉	216	4+	(Q8xC9).8S3	432,50
(Q₈×C₉).₉S₃ = C₃₆.₁₉D₆	φ: S₃/C₃ → C₂ ⊆ Out Q₈×C₉	432		(Q8xC9).9S3	432,194
(Q₈×C₉).₁₀S₃ = C₉×C₃⋊Q₁₆	φ: S₃/C₃ → C₂ ⊆ Out Q₈×C₉	144	4	(Q8xC9).10S3	432,159

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