Extensions 1→N→G→Q→1 with N=C₃² and Q=S₃

Direct product G=N×Q with N=C₃² and Q=S₃

		d	ρ	Label	ID
S₃×C₃²		18		S3xC3^2	54,12

Semidirect products G=N:Q with N=C₃² and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃²⋊₁S₃ = C₃²⋊C₆	φ: S₃/C₁ → S₃ ⊆ Aut C₃²	9	6+	C3^2:1S3	54,5
C₃²⋊₂S₃ = He₃⋊C₂	φ: S₃/C₁ → S₃ ⊆ Aut C₃²	9	3	C3^2:2S3	54,8
C₃²⋊₃S₃ = C₃×C₃⋊S₃	φ: S₃/C₃ → C₂ ⊆ Aut C₃²	18		C3^2:3S3	54,13
C₃²⋊₄S₃ = C₃³⋊C₂	φ: S₃/C₃ → C₂ ⊆ Aut C₃²	27		C3^2:4S3	54,14

Non-split extensions G=N.Q with N=C₃² and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃².S₃ = C₉⋊C₆	φ: S₃/C₁ → S₃ ⊆ Aut C₃²	9	6+	C3^2.S3	54,6
C₃².₂S₃ = C₃×D₉	φ: S₃/C₃ → C₂ ⊆ Aut C₃²	18	2	C3^2.2S3	54,3
C₃².₃S₃ = C₉⋊S₃	φ: S₃/C₃ → C₂ ⊆ Aut C₃²	27		C3^2.3S3	54,7

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