Extensions 1→N→G→Q→1 with N=C₃ and Q=C₃xS₃

Direct product G=NxQ with N=C₃ and Q=C₃xS₃

		d	ρ	Label	ID
S₃xC₃²		18		S3xC3^2	54,12

Semidirect products G=N:Q with N=C₃ and Q=C₃xS₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃:(C₃xS₃) = C₃xC₃:S₃	φ: C₃xS₃/C₃² → C₂ ⊆ Aut C₃	18		C3:(C3xS3)	54,13

Non-split extensions G=N.Q with N=C₃ and Q=C₃xS₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.₁(C₃xS₃) = C₃xD₉	φ: C₃xS₃/C₃² → C₂ ⊆ Aut C₃	18	2	C3.1(C3xS3)	54,3
C₃.₂(C₃xS₃) = C₃²:C₆	φ: C₃xS₃/C₃² → C₂ ⊆ Aut C₃	9	6+	C3.2(C3xS3)	54,5
C₃.₃(C₃xS₃) = C₉:C₆	φ: C₃xS₃/C₃² → C₂ ⊆ Aut C₃	9	6+	C3.3(C3xS3)	54,6
C₃.₄(C₃xS₃) = S₃xC₉	central extension (φ=1)	18	2	C3.4(C3xS3)	54,4

Extensions 1→N→G→Q→1 with N=C3 and Q=C3xS3