Extensions 1→N→G→Q→1 with N=C₆×A₄ and Q=S₃

Direct product G=N×Q with N=C₆×A₄ and Q=S₃

		d	ρ	Label	ID
S₃×C₆×A₄		36	6	S3xC6xA4	432,763

Semidirect products G=N:Q with N=C₆×A₄ and Q=S₃

extension	φ:Q→Out N	d	ρ	Label	ID
(C₆×A₄)⋊₁S₃ = C₂×C₃²⋊S₄	φ: S₃/C₁ → S₃ ⊆ Out C₆×A₄	18	3	(C6xA4):1S3	432,538
(C₆×A₄)⋊₂S₃ = C₂×C₆²⋊C₆	φ: S₃/C₁ → S₃ ⊆ Out C₆×A₄	18	6+	(C6xA4):2S3	432,542
(C₆×A₄)⋊₃S₃ = C₆×C₃⋊S₄	φ: S₃/C₃ → C₂ ⊆ Out C₆×A₄	36	6	(C6xA4):3S3	432,761
(C₆×A₄)⋊₄S₃ = C₂×C₃²⋊₄S₄	φ: S₃/C₃ → C₂ ⊆ Out C₆×A₄	54		(C6xA4):4S3	432,762
(C₆×A₄)⋊₅S₃ = C₂×A₄×C₃⋊S₃	φ: S₃/C₃ → C₂ ⊆ Out C₆×A₄	54		(C6xA4):5S3	432,764

Non-split extensions G=N.Q with N=C₆×A₄ and Q=S₃

extension	φ:Q→Out N	d	ρ	Label	ID
(C₆×A₄).₁S₃ = C₆²⋊₆Dic₃	φ: S₃/C₁ → S₃ ⊆ Out C₆×A₄	36	3	(C6xA4).1S3	432,260
(C₆×A₄).₂S₃ = Dic₉⋊A₄	φ: S₃/C₁ → S₃ ⊆ Out C₆×A₄	108	6-	(C6xA4).2S3	432,265
(C₆×A₄).₃S₃ = C₆²⋊₄C₁₂	φ: S₃/C₁ → S₃ ⊆ Out C₆×A₄	36	6-	(C6xA4).3S3	432,272
(C₆×A₄).₄S₃ = C₂×D₉⋊A₄	φ: S₃/C₁ → S₃ ⊆ Out C₆×A₄	54	6+	(C6xA4).4S3	432,539
(C₆×A₄).₅S₃ = A₄⋊Dic₉	φ: S₃/C₃ → C₂ ⊆ Out C₆×A₄	108	6-	(C6xA4).5S3	432,254
(C₆×A₄).₆S₃ = A₄×Dic₉	φ: S₃/C₃ → C₂ ⊆ Out C₆×A₄	108	6-	(C6xA4).6S3	432,266
(C₆×A₄).₇S₃ = C₂×C₉⋊S₄	φ: S₃/C₃ → C₂ ⊆ Out C₆×A₄	54	6+	(C6xA4).7S3	432,536
(C₆×A₄).₈S₃ = C₂×A₄×D₉	φ: S₃/C₃ → C₂ ⊆ Out C₆×A₄	54	6+	(C6xA4).8S3	432,540
(C₆×A₄).₉S₃ = C₃×C₆.₇S₄	φ: S₃/C₃ → C₂ ⊆ Out C₆×A₄	36	6	(C6xA4).9S3	432,618
(C₆×A₄).₁₀S₃ = C₆²⋊₁₀Dic₃	φ: S₃/C₃ → C₂ ⊆ Out C₆×A₄	108		(C6xA4).10S3	432,621
(C₆×A₄).₁₁S₃ = A₄×C₃⋊Dic₃	φ: S₃/C₃ → C₂ ⊆ Out C₆×A₄	108		(C6xA4).11S3	432,627
(C₆×A₄).₁₂S₃ = C₃×Dic₃×A₄	φ: trivial image	36	6	(C6xA4).12S3	432,624

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁