Extensions 1→N→G→Q→1 with N=C₃²xC₆ and Q=S₃

Direct product G=NxQ with N=C₃²xC₆ and Q=S₃

		d	ρ	Label	ID
S₃xC₃²xC₆		108		S3xC3^2xC6	324,172

Semidirect products G=N:Q with N=C₃²xC₆ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₃²xC₆):₁S₃ = C₂xC₃wrS₃	φ: S₃/C₁ → S₃ ⊆ Aut C₃²xC₆	18	3	(C3^2xC6):1S3	324,68
(C₃²xC₆):₂S₃ = C₂xC₃³:S₃	φ: S₃/C₁ → S₃ ⊆ Aut C₃²xC₆	18	6+	(C3^2xC6):2S3	324,77
(C₃²xC₆):₃S₃ = C₆xC₃²:C₆	φ: S₃/C₁ → S₃ ⊆ Aut C₃²xC₆	36	6	(C3^2xC6):3S3	324,138
(C₃²xC₆):₄S₃ = C₂xHe₃:₄S₃	φ: S₃/C₁ → S₃ ⊆ Aut C₃²xC₆	54		(C3^2xC6):4S3	324,144
(C₃²xC₆):₅S₃ = C₆xHe₃:C₂	φ: S₃/C₁ → S₃ ⊆ Aut C₃²xC₆	54		(C3^2xC6):5S3	324,145
(C₃²xC₆):₆S₃ = C₂xHe₃:₅S₃	φ: S₃/C₁ → S₃ ⊆ Aut C₃²xC₆	36	6	(C3^2xC6):6S3	324,150
(C₃²xC₆):₇S₃ = C₃:S₃xC₃xC₆	φ: S₃/C₃ → C₂ ⊆ Aut C₃²xC₆	36		(C3^2xC6):7S3	324,173
(C₃²xC₆):₈S₃ = C₆xC₃³:C₂	φ: S₃/C₃ → C₂ ⊆ Aut C₃²xC₆	108		(C3^2xC6):8S3	324,174
(C₃²xC₆):₉S₃ = C₂xC₃⁴:C₂	φ: S₃/C₃ → C₂ ⊆ Aut C₃²xC₆	162		(C3^2xC6):9S3	324,175

Non-split extensions G=N.Q with N=C₃²xC₆ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₃²xC₆).₁S₃ = C₃²:Dic₉	φ: S₃/C₁ → S₃ ⊆ Aut C₃²xC₆	108		(C3^2xC6).1S3	324,8
(C₃²xC₆).₂S₃ = He₃:C₁₂	φ: S₃/C₁ → S₃ ⊆ Aut C₃²xC₆	36	3	(C3^2xC6).2S3	324,13
(C₃²xC₆).₃S₃ = C₃²:₂Dic₉	φ: S₃/C₁ → S₃ ⊆ Aut C₃²xC₆	36	6	(C3^2xC6).3S3	324,20
(C₃²xC₆).₄S₃ = C₃³:Dic₃	φ: S₃/C₁ → S₃ ⊆ Aut C₃²xC₆	36	6-	(C3^2xC6).4S3	324,22
(C₃²xC₆).₅S₃ = C₂xC₃²:D₉	φ: S₃/C₁ → S₃ ⊆ Aut C₃²xC₆	54		(C3^2xC6).5S3	324,63
(C₃²xC₆).₆S₃ = C₂xC₃²:₂D₉	φ: S₃/C₁ → S₃ ⊆ Aut C₃²xC₆	36	6	(C3^2xC6).6S3	324,75
(C₃²xC₆).₇S₃ = C₃xC₃²:C₁₂	φ: S₃/C₁ → S₃ ⊆ Aut C₃²xC₆	36	6	(C3^2xC6).7S3	324,92
(C₃²xC₆).₈S₃ = C₃xC₉:C₁₂	φ: S₃/C₁ → S₃ ⊆ Aut C₃²xC₆	36	6	(C3^2xC6).8S3	324,94
(C₃²xC₆).₉S₃ = C₃³:₄C₁₂	φ: S₃/C₁ → S₃ ⊆ Aut C₃²xC₆	108		(C3^2xC6).9S3	324,98
(C₃²xC₆).₁₀S₃ = C₃xHe₃:₃C₄	φ: S₃/C₁ → S₃ ⊆ Aut C₃²xC₆	108		(C3^2xC6).10S3	324,99
(C₃²xC₆).₁₁S₃ = C₃³.Dic₃	φ: S₃/C₁ → S₃ ⊆ Aut C₃²xC₆	108		(C3^2xC6).11S3	324,100
(C₃²xC₆).₁₂S₃ = He₃:₆Dic₃	φ: S₃/C₁ → S₃ ⊆ Aut C₃²xC₆	36	6	(C3^2xC6).12S3	324,104
(C₃²xC₆).₁₃S₃ = C₆xC₉:C₆	φ: S₃/C₁ → S₃ ⊆ Aut C₃²xC₆	36	6	(C3^2xC6).13S3	324,140
(C₃²xC₆).₁₄S₃ = C₂xC₃³.S₃	φ: S₃/C₁ → S₃ ⊆ Aut C₃²xC₆	54		(C3^2xC6).14S3	324,146
(C₃²xC₆).₁₅S₃ = C₃²xDic₉	φ: S₃/C₃ → C₂ ⊆ Aut C₃²xC₆	108		(C3^2xC6).15S3	324,90
(C₃²xC₆).₁₆S₃ = C₃xC₉:Dic₃	φ: S₃/C₃ → C₂ ⊆ Aut C₃²xC₆	108		(C3^2xC6).16S3	324,96
(C₃²xC₆).₁₇S₃ = C₃²:₅Dic₉	φ: S₃/C₃ → C₂ ⊆ Aut C₃²xC₆	324		(C3^2xC6).17S3	324,103
(C₃²xC₆).₁₈S₃ = D₉xC₃xC₆	φ: S₃/C₃ → C₂ ⊆ Aut C₃²xC₆	108		(C3^2xC6).18S3	324,136
(C₃²xC₆).₁₉S₃ = C₆xC₉:S₃	φ: S₃/C₃ → C₂ ⊆ Aut C₃²xC₆	108		(C3^2xC6).19S3	324,142
(C₃²xC₆).₂₀S₃ = C₂xC₃²:₄D₉	φ: S₃/C₃ → C₂ ⊆ Aut C₃²xC₆	162		(C3^2xC6).20S3	324,149
(C₃²xC₆).₂₁S₃ = C₃²xC₃:Dic₃	φ: S₃/C₃ → C₂ ⊆ Aut C₃²xC₆	36		(C3^2xC6).21S3	324,156
(C₃²xC₆).₂₂S₃ = C₃xC₃³:₅C₄	φ: S₃/C₃ → C₂ ⊆ Aut C₃²xC₆	108		(C3^2xC6).22S3	324,157
(C₃²xC₆).₂₃S₃ = C₃⁴:₈C₄	φ: S₃/C₃ → C₂ ⊆ Aut C₃²xC₆	324		(C3^2xC6).23S3	324,158
(C₃²xC₆).₂₄S₃ = Dic₃xC₃³	central extension (φ=1)	108		(C3^2xC6).24S3	324,155

Extensions 1→N→G→Q→1 with N=C32xC6 and Q=S3

Extensions 1→N→G→Q→1 with N=C₃²xC₆ and Q=S₃