Extensions 1→N→G→Q→1 with N=C₃² and Q=C₃xS₃

Direct product G=NxQ with N=C₃² and Q=C₃xS₃

		d	ρ	Label	ID
S₃xC₃³		54		S3xC3^3	162,51

Semidirect products G=N:Q with N=C₃² and Q=C₃xS₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃²:₁(C₃xS₃) = C₃xC₃²:C₆	φ: C₃xS₃/C₃ → S₃ ⊆ Aut C₃²	18	6	C3^2:1(C3xS3)	162,34
C₃²:₂(C₃xS₃) = C₃xHe₃:C₂	φ: C₃xS₃/C₃ → S₃ ⊆ Aut C₃²	27		C3^2:2(C3xS3)	162,41
C₃²:₃(C₃xS₃) = He₃:₄S₃	φ: C₃xS₃/C₃ → C₆ ⊆ Aut C₃²	27		C3^2:3(C3xS3)	162,40
C₃²:₄(C₃xS₃) = S₃xHe₃	φ: C₃xS₃/S₃ → C₃ ⊆ Aut C₃²	18	6	C3^2:4(C3xS3)	162,35
C₃²:₅(C₃xS₃) = C₃²xC₃:S₃	φ: C₃xS₃/C₃² → C₂ ⊆ Aut C₃²	18		C3^2:5(C3xS3)	162,52
C₃²:₆(C₃xS₃) = C₃xC₃³:C₂	φ: C₃xS₃/C₃² → C₂ ⊆ Aut C₃²	54		C3^2:6(C3xS3)	162,53

Non-split extensions G=N.Q with N=C₃² and Q=C₃xS₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃².₁(C₃xS₃) = C₃wrS₃	φ: C₃xS₃/C₃ → S₃ ⊆ Aut C₃²	9	3	C3^2.1(C3xS3)	162,10
C₃².₂(C₃xS₃) = He₃.C₆	φ: C₃xS₃/C₃ → S₃ ⊆ Aut C₃²	27	3	C3^2.2(C3xS3)	162,12
C₃².₃(C₃xS₃) = He₃.₂C₆	φ: C₃xS₃/C₃ → S₃ ⊆ Aut C₃²	27	3	C3^2.3(C3xS3)	162,14
C₃².₄(C₃xS₃) = C₃xC₉:C₆	φ: C₃xS₃/C₃ → S₃ ⊆ Aut C₃²	18	6	C3^2.4(C3xS3)	162,36
C₃².₅(C₃xS₃) = He₃.₄C₆	φ: C₃xS₃/C₃ → S₃ ⊆ Aut C₃²	27	3	C3^2.5(C3xS3)	162,44
C₃².₆(C₃xS₃) = C₃³:C₆	φ: C₃xS₃/C₃ → C₆ ⊆ Aut C₃²	9	6+	C3^2.6(C3xS3)	162,11
C₃².₇(C₃xS₃) = He₃.S₃	φ: C₃xS₃/C₃ → C₆ ⊆ Aut C₃²	27	6+	C3^2.7(C3xS3)	162,13
C₃².₈(C₃xS₃) = He₃.₂S₃	φ: C₃xS₃/C₃ → C₆ ⊆ Aut C₃²	27	6+	C3^2.8(C3xS3)	162,15
C₃².₉(C₃xS₃) = He₃.₄S₃	φ: C₃xS₃/C₃ → C₆ ⊆ Aut C₃²	27	6+	C3^2.9(C3xS3)	162,43
C₃².₁₀(C₃xS₃) = S₃x3_-¹⁺²	φ: C₃xS₃/S₃ → C₃ ⊆ Aut C₃²	18	6	C3^2.10(C3xS3)	162,37
C₃².₁₁(C₃xS₃) = C₉xD₉	φ: C₃xS₃/C₃² → C₂ ⊆ Aut C₃²	18	2	C3^2.11(C3xS3)	162,3
C₃².₁₂(C₃xS₃) = C₃²:C₁₈	φ: C₃xS₃/C₃² → C₂ ⊆ Aut C₃²	18	6	C3^2.12(C3xS3)	162,4
C₃².₁₃(C₃xS₃) = C₃²:D₉	φ: C₃xS₃/C₃² → C₂ ⊆ Aut C₃²	27		C3^2.13(C3xS3)	162,5
C₃².₁₄(C₃xS₃) = C₉:C₁₈	φ: C₃xS₃/C₃² → C₂ ⊆ Aut C₃²	18	6	C3^2.14(C3xS3)	162,6
C₃².₁₅(C₃xS₃) = C₃²xD₉	φ: C₃xS₃/C₃² → C₂ ⊆ Aut C₃²	54		C3^2.15(C3xS3)	162,32
C₃².₁₆(C₃xS₃) = C₃xC₉:S₃	φ: C₃xS₃/C₃² → C₂ ⊆ Aut C₃²	54		C3^2.16(C3xS3)	162,38
C₃².₁₇(C₃xS₃) = C₉xC₃:S₃	φ: C₃xS₃/C₃² → C₂ ⊆ Aut C₃²	54		C3^2.17(C3xS3)	162,39
C₃².₁₈(C₃xS₃) = C₃³.S₃	φ: C₃xS₃/C₃² → C₂ ⊆ Aut C₃²	27		C3^2.18(C3xS3)	162,42
C₃².₁₉(C₃xS₃) = S₃xC₃xC₉	central extension (φ=1)	54		C3^2.19(C3xS3)	162,33

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