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

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

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

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

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊(C₃×S₃) = C₃×C₃⋊S₃	φ: C₃×S₃/C₃² → C₂ ⊆ Aut C₃	18		C3:(C3xS3)	54,13

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

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.₁(C₃×S₃) = C₃×D₉	φ: C₃×S₃/C₃² → C₂ ⊆ Aut C₃	18	2	C3.1(C3xS3)	54,3
C₃.₂(C₃×S₃) = C₃²⋊C₆	φ: C₃×S₃/C₃² → C₂ ⊆ Aut C₃	9	6+	C3.2(C3xS3)	54,5
C₃.₃(C₃×S₃) = C₉⋊C₆	φ: C₃×S₃/C₃² → C₂ ⊆ Aut C₃	9	6+	C3.3(C3xS3)	54,6
C₃.₄(C₃×S₃) = S₃×C₉	central extension (φ=1)	18	2	C3.4(C3xS3)	54,4

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