Extensions 1→N→G→Q→1 with N=C₉ and Q=C₃×S₃

Direct product G=N×Q with N=C₉ and Q=C₃×S₃

		d	ρ	Label	ID
S₃×C₃×C₉		54		S3xC3xC9	162,33

Semidirect products G=N:Q with N=C₉ and Q=C₃×S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₉⋊(C₃×S₃) = C₃³.S₃	φ: C₃×S₃/C₃ → C₆ ⊆ Aut C₉	27		C9:(C3xS3)	162,42
C₉⋊₂(C₃×S₃) = S₃×3_-¹⁺²	φ: C₃×S₃/S₃ → C₃ ⊆ Aut C₉	18	6	C9:2(C3xS3)	162,37
C₉⋊₃(C₃×S₃) = C₃×C₉⋊S₃	φ: C₃×S₃/C₃² → C₂ ⊆ Aut C₉	54		C9:3(C3xS3)	162,38

Non-split extensions G=N.Q with N=C₉ and Q=C₃×S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₉.(C₃×S₃) = He₃.₄S₃	φ: C₃×S₃/C₃ → C₆ ⊆ Aut C₉	27	6+	C9.(C3xS3)	162,43
C₉.₂(C₃×S₃) = C₃×D₂₇	φ: C₃×S₃/C₃² → C₂ ⊆ Aut C₉	54	2	C9.2(C3xS3)	162,7
C₉.₃(C₃×S₃) = C₂₇⋊C₆	φ: C₃×S₃/C₃² → C₂ ⊆ Aut C₉	27	6+	C9.3(C3xS3)	162,9
C₉.₄(C₃×S₃) = S₃×C₂₇	central extension (φ=1)	54	2	C9.4(C3xS3)	162,8

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