Extensions 1→N→G→Q→1 with N=C₂²xC₆ and Q=S₃

Direct product G=NxQ with N=C₂²xC₆ and Q=S₃

		d	ρ	Label	ID
S₃xC₂²xC₆		48		S3xC2^2xC6	144,195

Semidirect products G=N:Q with N=C₂²xC₆ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂²xC₆):₁S₃ = C₆xS₄	φ: S₃/C₁ → S₃ ⊆ Aut C₂²xC₆	18	3	(C2^2xC6):1S3	144,188
(C₂²xC₆):₂S₃ = C₂xC₃:S₄	φ: S₃/C₁ → S₃ ⊆ Aut C₂²xC₆	18	6+	(C2^2xC6):2S3	144,189
(C₂²xC₆):₃S₃ = C₆xC₃:D₄	φ: S₃/C₃ → C₂ ⊆ Aut C₂²xC₆	24		(C2^2xC6):3S3	144,167
(C₂²xC₆):₄S₃ = C₂xC₃²:₇D₄	φ: S₃/C₃ → C₂ ⊆ Aut C₂²xC₆	72		(C2^2xC6):4S3	144,177
(C₂²xC₆):₅S₃ = C₂³xC₃:S₃	φ: S₃/C₃ → C₂ ⊆ Aut C₂²xC₆	72		(C2^2xC6):5S3	144,196

Non-split extensions G=N.Q with N=C₂²xC₆ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂²xC₆).₁S₃ = C₃xA₄:C₄	φ: S₃/C₁ → S₃ ⊆ Aut C₂²xC₆	36	3	(C2^2xC6).1S3	144,123
(C₂²xC₆).₂S₃ = C₆.S₄	φ: S₃/C₁ → S₃ ⊆ Aut C₂²xC₆	36	6-	(C2^2xC6).2S3	144,33
(C₂²xC₆).₃S₃ = C₂xC₃.S₄	φ: S₃/C₁ → S₃ ⊆ Aut C₂²xC₆	18	6+	(C2^2xC6).3S3	144,109
(C₂²xC₆).₄S₃ = C₆.₇S₄	φ: S₃/C₁ → S₃ ⊆ Aut C₂²xC₆	36	6-	(C2^2xC6).4S3	144,126
(C₂²xC₆).₅S₃ = C₃xC₆.D₄	φ: S₃/C₃ → C₂ ⊆ Aut C₂²xC₆	24		(C2^2xC6).5S3	144,84
(C₂²xC₆).₆S₃ = C₁₈.D₄	φ: S₃/C₃ → C₂ ⊆ Aut C₂²xC₆	72		(C2^2xC6).6S3	144,19
(C₂²xC₆).₇S₃ = C₂²xDic₉	φ: S₃/C₃ → C₂ ⊆ Aut C₂²xC₆	144		(C2^2xC6).7S3	144,45
(C₂²xC₆).₈S₃ = C₂xC₉:D₄	φ: S₃/C₃ → C₂ ⊆ Aut C₂²xC₆	72		(C2^2xC6).8S3	144,46
(C₂²xC₆).₉S₃ = C₆²:₅C₄	φ: S₃/C₃ → C₂ ⊆ Aut C₂²xC₆	72		(C2^2xC6).9S3	144,100
(C₂²xC₆).₁₀S₃ = C₂³xD₉	φ: S₃/C₃ → C₂ ⊆ Aut C₂²xC₆	72		(C2^2xC6).10S3	144,112
(C₂²xC₆).₁₁S₃ = C₂²xC₃:Dic₃	φ: S₃/C₃ → C₂ ⊆ Aut C₂²xC₆	144		(C2^2xC6).11S3	144,176
(C₂²xC₆).₁₂S₃ = Dic₃xC₂xC₆	central extension (φ=1)	48		(C2^2xC6).12S3	144,166

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