Extensions 1→N→G→Q→1 with N=C₃×C₆ and Q=S₃

Direct product G=N×Q with N=C₃×C₆ and Q=S₃

		d	ρ	Label	ID
S₃×C₃×C₆		36		S3xC3xC6	108,42

Semidirect products G=N:Q with N=C₃×C₆ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₃×C₆)⋊₁S₃ = C₂×C₃²⋊C₆	φ: S₃/C₁ → S₃ ⊆ Aut C₃×C₆	18	6+	(C3xC6):1S3	108,25
(C₃×C₆)⋊₂S₃ = C₂×He₃⋊C₂	φ: S₃/C₁ → S₃ ⊆ Aut C₃×C₆	18	3	(C3xC6):2S3	108,28
(C₃×C₆)⋊₃S₃ = C₆×C₃⋊S₃	φ: S₃/C₃ → C₂ ⊆ Aut C₃×C₆	36		(C3xC6):3S3	108,43
(C₃×C₆)⋊₄S₃ = C₂×C₃³⋊C₂	φ: S₃/C₃ → C₂ ⊆ Aut C₃×C₆	54		(C3xC6):4S3	108,44

Non-split extensions G=N.Q with N=C₃×C₆ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₃×C₆).₁S₃ = C₃²⋊C₁₂	φ: S₃/C₁ → S₃ ⊆ Aut C₃×C₆	36	6-	(C3xC6).1S3	108,8
(C₃×C₆).₂S₃ = C₉⋊C₁₂	φ: S₃/C₁ → S₃ ⊆ Aut C₃×C₆	36	6-	(C3xC6).2S3	108,9
(C₃×C₆).₃S₃ = He₃⋊₃C₄	φ: S₃/C₁ → S₃ ⊆ Aut C₃×C₆	36	3	(C3xC6).3S3	108,11
(C₃×C₆).₄S₃ = C₂×C₉⋊C₆	φ: S₃/C₁ → S₃ ⊆ Aut C₃×C₆	18	6+	(C3xC6).4S3	108,26
(C₃×C₆).₅S₃ = C₃×Dic₉	φ: S₃/C₃ → C₂ ⊆ Aut C₃×C₆	36	2	(C3xC6).5S3	108,6
(C₃×C₆).₆S₃ = C₉⋊Dic₃	φ: S₃/C₃ → C₂ ⊆ Aut C₃×C₆	108		(C3xC6).6S3	108,10
(C₃×C₆).₇S₃ = C₆×D₉	φ: S₃/C₃ → C₂ ⊆ Aut C₃×C₆	36	2	(C3xC6).7S3	108,23
(C₃×C₆).₈S₃ = C₂×C₉⋊S₃	φ: S₃/C₃ → C₂ ⊆ Aut C₃×C₆	54		(C3xC6).8S3	108,27
(C₃×C₆).₉S₃ = C₃×C₃⋊Dic₃	φ: S₃/C₃ → C₂ ⊆ Aut C₃×C₆	36		(C3xC6).9S3	108,33
(C₃×C₆).₁₀S₃ = C₃³⋊₅C₄	φ: S₃/C₃ → C₂ ⊆ Aut C₃×C₆	108		(C3xC6).10S3	108,34
(C₃×C₆).₁₁S₃ = C₃²×Dic₃	central extension (φ=1)	36		(C3xC6).11S3	108,32

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