Extensions 1→N→G→Q→1 with N=C₃² and Q=S₃²

Direct product G=N×Q with N=C₃² and Q=S₃²

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

Semidirect products G=N:Q with N=C₃² and Q=S₃²

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃²⋊₁S₃² = He₃⋊₅D₆	φ: S₃²/C₃ → D₆ ⊆ Aut C₃²	18	12+	C3^2:1S3^2	324,121
C₃²⋊₂S₃² = He₃⋊₆D₆	φ: S₃²/C₃ → D₆ ⊆ Aut C₃²	27		C3^2:2S3^2	324,124
C₃²⋊₃S₃² = S₃×C₃²⋊C₆	φ: S₃²/S₃ → S₃ ⊆ Aut C₃²	18	12+	C3^2:3S3^2	324,116
C₃²⋊₄S₃² = S₃×He₃⋊C₂	φ: S₃²/S₃ → S₃ ⊆ Aut C₃²	18	6	C3^2:4S3^2	324,122
C₃²⋊₅S₃² = C₃⋊S₃²	φ: S₃²/C₃² → C₂² ⊆ Aut C₃²	18		C3^2:5S3^2	324,169
C₃²⋊₆S₃² = C₃³⋊₁₇D₆	φ: S₃²/C₃² → C₂² ⊆ Aut C₃²	36		C3^2:6S3^2	324,170
C₃²⋊₇S₃² = C₃×S₃×C₃⋊S₃	φ: S₃²/C₃×S₃ → C₂ ⊆ Aut C₃²	36		C3^2:7S3^2	324,166
C₃²⋊₈S₃² = S₃×C₃³⋊C₂	φ: S₃²/C₃×S₃ → C₂ ⊆ Aut C₃²	54		C3^2:8S3^2	324,168
C₃²⋊₉S₃² = C₃×C₃²⋊₄D₆	φ: S₃²/C₃⋊S₃ → C₂ ⊆ Aut C₃²	12	4	C3^2:9S3^2	324,167

Non-split extensions G=N.Q with N=C₃² and Q=S₃²

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃².₁S₃² = He₃⋊D₆	φ: S₃²/C₃ → D₆ ⊆ Aut C₃²	9	6+	C3^2.1S3^2	324,39
C₃².₂S₃² = He₃.D₆	φ: S₃²/C₃ → D₆ ⊆ Aut C₃²	27	6+	C3^2.2S3^2	324,40
C₃².₃S₃² = He₃.₂D₆	φ: S₃²/C₃ → D₆ ⊆ Aut C₃²	27	6+	C3^2.3S3^2	324,41
C₃².₄S₃² = He₃.₆D₆	φ: S₃²/C₃ → D₆ ⊆ Aut C₃²	27	6+	C3^2.4S3^2	324,125
C₃².₅S₃² = S₃×C₉⋊C₆	φ: S₃²/S₃ → S₃ ⊆ Aut C₃²	18	12+	C3^2.5S3^2	324,118
C₃².₆S₃² = D₉²	φ: S₃²/C₃² → C₂² ⊆ Aut C₃²	18	4+	C3^2.6S3^2	324,36
C₃².₇S₃² = C₃²⋊D₁₈	φ: S₃²/C₃² → C₂² ⊆ Aut C₃²	18	12+	C3^2.7S3^2	324,37
C₃².₈S₃² = D₉×C₃⋊S₃	φ: S₃²/C₃² → C₂² ⊆ Aut C₃²	54		C3^2.8S3^2	324,119
C₃².₉S₃² = C₃²⋊₅D₁₈	φ: S₃²/C₃² → C₂² ⊆ Aut C₃²	36	4	C3^2.9S3^2	324,123
C₃².₁₀S₃² = C₃×S₃×D₉	φ: S₃²/C₃×S₃ → C₂ ⊆ Aut C₃²	36	4	C3^2.10S3^2	324,114
C₃².₁₁S₃² = S₃×C₉⋊S₃	φ: S₃²/C₃×S₃ → C₂ ⊆ Aut C₃²	54		C3^2.11S3^2	324,120
C₃².₁₂S₃² = C₃×C₃²⋊D₆	φ: S₃²/C₃⋊S₃ → C₂ ⊆ Aut C₃²	18	6	C3^2.12S3^2	324,117

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