Extensions 1→N→G→Q→1 with N=C₃ and Q=C₃×S₃²

Direct product G=N×Q with N=C₃ and Q=C₃×S₃²

		d	ρ	Label	ID
S₃²×C₃²		36		S3^2xC3^2	324,165

Semidirect products G=N:Q with N=C₃ and Q=C₃×S₃²

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊₁(C₃×S₃²) = C₃×S₃×C₃⋊S₃	φ: C₃×S₃²/S₃×C₃² → C₂ ⊆ Aut C₃	36		C3:1(C3xS3^2)	324,166
C₃⋊₂(C₃×S₃²) = C₃×C₃²⋊₄D₆	φ: C₃×S₃²/C₃×C₃⋊S₃ → C₂ ⊆ Aut C₃	12	4	C3:2(C3xS3^2)	324,167

Non-split extensions G=N.Q with N=C₃ and Q=C₃×S₃²

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.₁(C₃×S₃²) = C₃×S₃×D₉	φ: C₃×S₃²/S₃×C₃² → C₂ ⊆ Aut C₃	36	4	C3.1(C3xS3^2)	324,114
C₃.₂(C₃×S₃²) = S₃×C₃²⋊C₆	φ: C₃×S₃²/S₃×C₃² → C₂ ⊆ Aut C₃	18	12+	C3.2(C3xS3^2)	324,116
C₃.₃(C₃×S₃²) = S₃×C₉⋊C₆	φ: C₃×S₃²/S₃×C₃² → C₂ ⊆ Aut C₃	18	12+	C3.3(C3xS3^2)	324,118
C₃.₄(C₃×S₃²) = C₃×C₃²⋊D₆	φ: C₃×S₃²/C₃×C₃⋊S₃ → C₂ ⊆ Aut C₃	18	6	C3.4(C3xS3^2)	324,117
C₃.₅(C₃×S₃²) = S₃²×C₉	central extension (φ=1)	36	4	C3.5(C3xS3^2)	324,115

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