Extensions 1→N→G→Q→1 with N=C₃×M₄(2) and Q=S₃

Direct product G=N×Q with N=C₃×M₄(2) and Q=S₃

		d	ρ	Label	ID
C₃×S₃×M₄(2)		48	4	C3xS3xM4(2)	288,677

Semidirect products G=N:Q with N=C₃×M₄(2) and Q=S₃

extension	φ:Q→Out N	d	ρ	Label	ID
(C₃×M₄(2))⋊₁S₃ = C₂₄⋊₃D₆	φ: S₃/C₃ → C₂ ⊆ Out C₃×M₄(2)	72		(C3xM4(2)):1S3	288,765
(C₃×M₄(2))⋊₂S₃ = C₂₄.₅D₆	φ: S₃/C₃ → C₂ ⊆ Out C₃×M₄(2)	144		(C3xM4(2)):2S3	288,766
(C₃×M₄(2))⋊₃S₃ = C₃×C₈⋊D₆	φ: S₃/C₃ → C₂ ⊆ Out C₃×M₄(2)	48	4	(C3xM4(2)):3S3	288,679
(C₃×M₄(2))⋊₄S₃ = C₃×C₈.D₆	φ: S₃/C₃ → C₂ ⊆ Out C₃×M₄(2)	48	4	(C3xM4(2)):4S3	288,680
(C₃×M₄(2))⋊₅S₃ = M₄(2)×C₃⋊S₃	φ: S₃/C₃ → C₂ ⊆ Out C₃×M₄(2)	72		(C3xM4(2)):5S3	288,763
(C₃×M₄(2))⋊₆S₃ = C₂₄.₄₇D₆	φ: S₃/C₃ → C₂ ⊆ Out C₃×M₄(2)	144		(C3xM4(2)):6S3	288,764
(C₃×M₄(2))⋊₇S₃ = C₃×C₁₂.₄₆D₄	φ: S₃/C₃ → C₂ ⊆ Out C₃×M₄(2)	48	4	(C3xM4(2)):7S3	288,257
(C₃×M₄(2))⋊₈S₃ = C₃×D₁₂⋊C₄	φ: S₃/C₃ → C₂ ⊆ Out C₃×M₄(2)	48	4	(C3xM4(2)):8S3	288,259
(C₃×M₄(2))⋊₉S₃ = C₁₂.₁₉D₁₂	φ: S₃/C₃ → C₂ ⊆ Out C₃×M₄(2)	72		(C3xM4(2)):9S3	288,298
(C₃×M₄(2))⋊₁₀S₃ = C₆².₃₇D₄	φ: S₃/C₃ → C₂ ⊆ Out C₃×M₄(2)	72		(C3xM4(2)):10S3	288,300
(C₃×M₄(2))⋊₁₁S₃ = C₃×D₁₂.C₄	φ: trivial image	48	4	(C3xM4(2)):11S3	288,678

Non-split extensions G=N.Q with N=C₃×M₄(2) and Q=S₃

extension	φ:Q→Out N	d	ρ	Label	ID
(C₃×M₄(2)).₁S₃ = C₈⋊D₁₈	φ: S₃/C₃ → C₂ ⊆ Out C₃×M₄(2)	72	4+	(C3xM4(2)).1S3	288,118
(C₃×M₄(2)).₂S₃ = C₈.D₁₈	φ: S₃/C₃ → C₂ ⊆ Out C₃×M₄(2)	144	4-	(C3xM4(2)).2S3	288,119
(C₃×M₄(2)).₃S₃ = M₄(2)×D₉	φ: S₃/C₃ → C₂ ⊆ Out C₃×M₄(2)	72	4	(C3xM4(2)).3S3	288,116
(C₃×M₄(2)).₄S₃ = D₃₆.C₄	φ: S₃/C₃ → C₂ ⊆ Out C₃×M₄(2)	144	4	(C3xM4(2)).4S3	288,117
(C₃×M₄(2)).₅S₃ = C₃₆.₅₃D₄	φ: S₃/C₃ → C₂ ⊆ Out C₃×M₄(2)	144	4	(C3xM4(2)).5S3	288,29
(C₃×M₄(2)).₆S₃ = C₄.D₃₆	φ: S₃/C₃ → C₂ ⊆ Out C₃×M₄(2)	144	4-	(C3xM4(2)).6S3	288,30
(C₃×M₄(2)).₇S₃ = C₃₆.₄₈D₄	φ: S₃/C₃ → C₂ ⊆ Out C₃×M₄(2)	72	4+	(C3xM4(2)).7S3	288,31
(C₃×M₄(2)).₈S₃ = Dic₁₈⋊C₄	φ: S₃/C₃ → C₂ ⊆ Out C₃×M₄(2)	72	4	(C3xM4(2)).8S3	288,32
(C₃×M₄(2)).₉S₃ = C₃×C₁₂.₅₃D₄	φ: S₃/C₃ → C₂ ⊆ Out C₃×M₄(2)	48	4	(C3xM4(2)).9S3	288,256
(C₃×M₄(2)).₁₀S₃ = C₃×C₁₂.₄₇D₄	φ: S₃/C₃ → C₂ ⊆ Out C₃×M₄(2)	48	4	(C3xM4(2)).10S3	288,258
(C₃×M₄(2)).₁₁S₃ = C₆².₈Q₈	φ: S₃/C₃ → C₂ ⊆ Out C₃×M₄(2)	144		(C3xM4(2)).11S3	288,297
(C₃×M₄(2)).₁₂S₃ = C₁₂.₂₀D₁₂	φ: S₃/C₃ → C₂ ⊆ Out C₃×M₄(2)	144		(C3xM4(2)).12S3	288,299

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