Extensions 1→N→G→Q→1 with N=C₂³xC₆ and Q=S₃

Direct product G=NxQ with N=C₂³xC₆ and Q=S₃

		d	ρ	Label	ID
S₃xC₂³xC₆		96		S3xC2^3xC6	288,1043

Semidirect products G=N:Q with N=C₂³xC₆ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂³xC₆):₁S₃ = C₃xA₄:D₄	φ: S₃/C₁ → S₃ ⊆ Aut C₂³xC₆	36	6	(C2^3xC6):1S3	288,906
(C₂³xC₆):₂S₃ = C₂xC₆xS₄	φ: S₃/C₁ → S₃ ⊆ Aut C₂³xC₆	36		(C2^3xC6):2S3	288,1033
(C₂³xC₆):₃S₃ = C₃xC₂²:S₄	φ: S₃/C₁ → S₃ ⊆ Aut C₂³xC₆	24	6	(C2^3xC6):3S3	288,1035
(C₂³xC₆):₄S₃ = (C₂xC₆):₄S₄	φ: S₃/C₁ → S₃ ⊆ Aut C₂³xC₆	36	6	(C2^3xC6):4S3	288,917
(C₂³xC₆):₅S₃ = C₂²xC₃:S₄	φ: S₃/C₁ → S₃ ⊆ Aut C₂³xC₆	36		(C2^3xC6):5S3	288,1034
(C₂³xC₆):₆S₃ = (C₂xC₆):S₄	φ: S₃/C₁ → S₃ ⊆ Aut C₂³xC₆	24	6	(C2^3xC6):6S3	288,1036
(C₂³xC₆):₇S₃ = C₃xC₂⁴:₄S₃	φ: S₃/C₃ → C₂ ⊆ Aut C₂³xC₆	24		(C2^3xC6):7S3	288,724
(C₂³xC₆):₈S₃ = C₂xC₆xC₃:D₄	φ: S₃/C₃ → C₂ ⊆ Aut C₂³xC₆	48		(C2^3xC6):8S3	288,1002
(C₂³xC₆):₉S₃ = C₆²:₂₄D₄	φ: S₃/C₃ → C₂ ⊆ Aut C₂³xC₆	72		(C2^3xC6):9S3	288,810
(C₂³xC₆):₁₀S₃ = C₂²xC₃²:₇D₄	φ: S₃/C₃ → C₂ ⊆ Aut C₂³xC₆	144		(C2^3xC6):10S3	288,1017
(C₂³xC₆):₁₁S₃ = C₂⁴xC₃:S₃	φ: S₃/C₃ → C₂ ⊆ Aut C₂³xC₆	144		(C2^3xC6):11S3	288,1044

Non-split extensions G=N.Q with N=C₂³xC₆ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂³xC₆).₁S₃ = C₆xA₄:C₄	φ: S₃/C₁ → S₃ ⊆ Aut C₂³xC₆	72		(C2^3xC6).1S3	288,905
(C₂³xC₆).₂S₃ = C₂xC₆.S₄	φ: S₃/C₁ → S₃ ⊆ Aut C₂³xC₆	72		(C2^3xC6).2S3	288,341
(C₂³xC₆).₃S₃ = C₂³.D₁₈	φ: S₃/C₁ → S₃ ⊆ Aut C₂³xC₆	36	6	(C2^3xC6).3S3	288,342
(C₂³xC₆).₄S₃ = C₂²xC₃.S₄	φ: S₃/C₁ → S₃ ⊆ Aut C₂³xC₆	36		(C2^3xC6).4S3	288,835
(C₂³xC₆).₅S₃ = C₂⁴:D₉	φ: S₃/C₁ → S₃ ⊆ Aut C₂³xC₆	36	6	(C2^3xC6).5S3	288,836
(C₂³xC₆).₆S₃ = C₂xC₆.₇S₄	φ: S₃/C₁ → S₃ ⊆ Aut C₂³xC₆	72		(C2^3xC6).6S3	288,916
(C₂³xC₆).₇S₃ = C₆xC₆.D₄	φ: S₃/C₃ → C₂ ⊆ Aut C₂³xC₆	48		(C2^3xC6).7S3	288,723
(C₂³xC₆).₈S₃ = C₂xC₁₈.D₄	φ: S₃/C₃ → C₂ ⊆ Aut C₂³xC₆	144		(C2^3xC6).8S3	288,162
(C₂³xC₆).₉S₃ = C₂⁴:₄D₉	φ: S₃/C₃ → C₂ ⊆ Aut C₂³xC₆	72		(C2^3xC6).9S3	288,163
(C₂³xC₆).₁₀S₃ = C₂³xDic₉	φ: S₃/C₃ → C₂ ⊆ Aut C₂³xC₆	288		(C2^3xC6).10S3	288,365
(C₂³xC₆).₁₁S₃ = C₂²xC₉:D₄	φ: S₃/C₃ → C₂ ⊆ Aut C₂³xC₆	144		(C2^3xC6).11S3	288,366
(C₂³xC₆).₁₂S₃ = C₂xC₆²:₅C₄	φ: S₃/C₃ → C₂ ⊆ Aut C₂³xC₆	144		(C2^3xC6).12S3	288,809
(C₂³xC₆).₁₃S₃ = C₂⁴xD₉	φ: S₃/C₃ → C₂ ⊆ Aut C₂³xC₆	144		(C2^3xC6).13S3	288,839
(C₂³xC₆).₁₄S₃ = C₂³xC₃:Dic₃	φ: S₃/C₃ → C₂ ⊆ Aut C₂³xC₆	288		(C2^3xC6).14S3	288,1016
(C₂³xC₆).₁₅S₃ = Dic₃xC₂²xC₆	central extension (φ=1)	96		(C2^3xC6).15S3	288,1001

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