Extensions 1→N→G→Q→1 with N=C₃ and Q=S₃×3_-¹⁺²

Direct product G=N×Q with N=C₃ and Q=S₃×3_-¹⁺²

		d	ρ	Label	ID
C₃×S₃×3_-¹⁺²		54		C3xS3xES-(3,1)	486,225

Semidirect products G=N:Q with N=C₃ and Q=S₃×3_-¹⁺²

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊(S₃×3_-¹⁺²) = C₃⋊S₃×3_-¹⁺²	φ: S₃×3_-¹⁺²/C₃×3_-¹⁺² → C₂ ⊆ Aut C₃	54		C3:(S3xES-(3,1))	486,233

Non-split extensions G=N.Q with N=C₃ and Q=S₃×3_-¹⁺²

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.₁(S₃×3_-¹⁺²) = D₉×3_-¹⁺²	φ: S₃×3_-¹⁺²/C₃×3_-¹⁺² → C₂ ⊆ Aut C₃	54	6	C3.1(S3xES-(3,1))	486,101
C₃.₂(S₃×3_-¹⁺²) = C₃⁴.C₆	φ: S₃×3_-¹⁺²/C₃×3_-¹⁺² → C₂ ⊆ Aut C₃	18	6	C3.2(S3xES-(3,1))	486,104
C₃.₃(S₃×3_-¹⁺²) = C₉⋊He₃⋊C₂	φ: S₃×3_-¹⁺²/C₃×3_-¹⁺² → C₂ ⊆ Aut C₃	54	6	C3.3(S3xES-(3,1))	486,107
C₃.₄(S₃×3_-¹⁺²) = D₉⋊3_-¹⁺²	φ: S₃×3_-¹⁺²/C₃×3_-¹⁺² → C₂ ⊆ Aut C₃	54	6	C3.4(S3xES-(3,1))	486,108
C₃.₅(S₃×3_-¹⁺²) = C₉²⋊₇C₆	φ: S₃×3_-¹⁺²/C₃×3_-¹⁺² → C₂ ⊆ Aut C₃	54	6	C3.5(S3xES-(3,1))	486,109
C₃.₆(S₃×3_-¹⁺²) = C₉²⋊₈C₆	φ: S₃×3_-¹⁺²/C₃×3_-¹⁺² → C₂ ⊆ Aut C₃	18	6	C3.6(S3xES-(3,1))	486,110
C₃.₇(S₃×3_-¹⁺²) = S₃×C₃²⋊C₉	central extension (φ=1)	54		C3.7(S3xES-(3,1))	486,95
C₃.₈(S₃×3_-¹⁺²) = S₃×C₉⋊C₉	central extension (φ=1)	162		C3.8(S3xES-(3,1))	486,97

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