Extensions 1→N→G→Q→1 with N=D₄×C₃² and Q=S₃

Direct product G=N×Q with N=D₄×C₃² and Q=S₃

		d	ρ	Label	ID
S₃×D₄×C₃²		72		S3xD4xC3^2	432,704

Semidirect products G=N:Q with N=D₄×C₃² and Q=S₃

extension	φ:Q→Out N	d	ρ	Label	ID
(D₄×C₃²)⋊₁S₃ = He₃⋊₆D₈	φ: S₃/C₁ → S₃ ⊆ Out D₄×C₃²	72	12+	(D4xC3^2):1S3	432,153
(D₄×C₃²)⋊₂S₃ = He₃⋊₇D₈	φ: S₃/C₁ → S₃ ⊆ Out D₄×C₃²	72	6	(D4xC3^2):2S3	432,192
(D₄×C₃²)⋊₃S₃ = D₄×C₃²⋊C₆	φ: S₃/C₁ → S₃ ⊆ Out D₄×C₃²	36	12+	(D4xC3^2):3S3	432,360
(D₄×C₃²)⋊₄S₃ = C₆².₁₃D₆	φ: S₃/C₁ → S₃ ⊆ Out D₄×C₃²	72	12-	(D4xC3^2):4S3	432,361
(D₄×C₃²)⋊₅S₃ = D₄×He₃⋊C₂	φ: S₃/C₁ → S₃ ⊆ Out D₄×C₃²	36	6	(D4xC3^2):5S3	432,390
(D₄×C₃²)⋊₆S₃ = C₆².₁₆D₆	φ: S₃/C₁ → S₃ ⊆ Out D₄×C₃²	72	6	(D4xC3^2):6S3	432,391
(D₄×C₃²)⋊₇S₃ = C₃×C₃²⋊₇D₈	φ: S₃/C₃ → C₂ ⊆ Out D₄×C₃²	72		(D4xC3^2):7S3	432,491
(D₄×C₃²)⋊₈S₃ = C₃³⋊₁₅D₈	φ: S₃/C₃ → C₂ ⊆ Out D₄×C₃²	216		(D4xC3^2):8S3	432,507
(D₄×C₃²)⋊₉S₃ = C₃×D₄×C₃⋊S₃	φ: S₃/C₃ → C₂ ⊆ Out D₄×C₃²	72		(D4xC3^2):9S3	432,714
(D₄×C₃²)⋊₁₀S₃ = C₃×C₁₂.D₆	φ: S₃/C₃ → C₂ ⊆ Out D₄×C₃²	72		(D4xC3^2):10S3	432,715
(D₄×C₃²)⋊₁₁S₃ = D₄×C₃³⋊C₂	φ: S₃/C₃ → C₂ ⊆ Out D₄×C₃²	108		(D4xC3^2):11S3	432,724
(D₄×C₃²)⋊₁₂S₃ = C₆².₁₀₀D₆	φ: S₃/C₃ → C₂ ⊆ Out D₄×C₃²	216		(D4xC3^2):12S3	432,725
(D₄×C₃²)⋊₁₃S₃ = C₃²×D₄⋊S₃	φ: S₃/C₃ → C₂ ⊆ Out D₄×C₃²	72		(D4xC3^2):13S3	432,475
(D₄×C₃²)⋊₁₄S₃ = C₃²×D₄⋊₂S₃	φ: trivial image	72		(D4xC3^2):14S3	432,705

Non-split extensions G=N.Q with N=D₄×C₃² and Q=S₃

extension	φ:Q→Out N	d	ρ	Label	ID
(D₄×C₃²).₁S₃ = He₃⋊₈SD₁₆	φ: S₃/C₁ → S₃ ⊆ Out D₄×C₃²	72	12-	(D4xC3^2).1S3	432,152
(D₄×C₃²).₂S₃ = Dic₁₈⋊C₆	φ: S₃/C₁ → S₃ ⊆ Out D₄×C₃²	72	12-	(D4xC3^2).2S3	432,154
(D₄×C₃²).₃S₃ = D₃₆⋊C₆	φ: S₃/C₁ → S₃ ⊆ Out D₄×C₃²	72	12+	(D4xC3^2).3S3	432,155
(D₄×C₃²).₄S₃ = He₃⋊₉SD₁₆	φ: S₃/C₁ → S₃ ⊆ Out D₄×C₃²	72	6	(D4xC3^2).4S3	432,193
(D₄×C₃²).₅S₃ = D₄×C₉⋊C₆	φ: S₃/C₁ → S₃ ⊆ Out D₄×C₃²	36	12+	(D4xC3^2).5S3	432,362
(D₄×C₃²).₆S₃ = Dic₁₈⋊₂C₆	φ: S₃/C₁ → S₃ ⊆ Out D₄×C₃²	72	12-	(D4xC3^2).6S3	432,363
(D₄×C₃²).₇S₃ = C₃×D₄.D₉	φ: S₃/C₃ → C₂ ⊆ Out D₄×C₃²	72	4	(D4xC3^2).7S3	432,148
(D₄×C₃²).₈S₃ = C₃×D₄⋊D₉	φ: S₃/C₃ → C₂ ⊆ Out D₄×C₃²	72	4	(D4xC3^2).8S3	432,149
(D₄×C₃²).₉S₃ = C₃₆.₁₇D₆	φ: S₃/C₃ → C₂ ⊆ Out D₄×C₃²	216		(D4xC3^2).9S3	432,190
(D₄×C₃²).₁₀S₃ = C₃₆.₁₈D₆	φ: S₃/C₃ → C₂ ⊆ Out D₄×C₃²	216		(D4xC3^2).10S3	432,191
(D₄×C₃²).₁₁S₃ = C₃×D₄×D₉	φ: S₃/C₃ → C₂ ⊆ Out D₄×C₃²	72	4	(D4xC3^2).11S3	432,356
(D₄×C₃²).₁₂S₃ = C₃×D₄⋊₂D₉	φ: S₃/C₃ → C₂ ⊆ Out D₄×C₃²	72	4	(D4xC3^2).12S3	432,357
(D₄×C₃²).₁₃S₃ = D₄×C₉⋊S₃	φ: S₃/C₃ → C₂ ⊆ Out D₄×C₃²	108		(D4xC3^2).13S3	432,388
(D₄×C₃²).₁₄S₃ = C₃₆.₂₇D₆	φ: S₃/C₃ → C₂ ⊆ Out D₄×C₃²	216		(D4xC3^2).14S3	432,389
(D₄×C₃²).₁₅S₃ = C₃×C₃²⋊₉SD₁₆	φ: S₃/C₃ → C₂ ⊆ Out D₄×C₃²	72		(D4xC3^2).15S3	432,492
(D₄×C₃²).₁₆S₃ = C₃³⋊₂₄SD₁₆	φ: S₃/C₃ → C₂ ⊆ Out D₄×C₃²	216		(D4xC3^2).16S3	432,508
(D₄×C₃²).₁₇S₃ = C₃²×D₄.S₃	φ: S₃/C₃ → C₂ ⊆ Out D₄×C₃²	72		(D4xC3^2).17S3	432,476

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