Extensions 1→N→G→Q→1 with N=C₃ and Q=He₃.S₃

Direct product G=N×Q with N=C₃ and Q=He₃.S₃

		d	ρ	Label	ID
C₃×He₃.S₃		54	6	C3xHe3.S3	486,119

Semidirect products G=N:Q with N=C₃ and Q=He₃.S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊(He₃.S₃) = C₃²⋊₄D₉⋊C₃	φ: He₃.S₃/He₃.C₃ → C₂ ⊆ Aut C₃	81		C3:(He3.S3)	486,170

Non-split extensions G=N.Q with N=C₃ and Q=He₃.S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.(He₃.S₃) = He₃⋊D₉	φ: He₃.S₃/He₃.C₃ → C₂ ⊆ Aut C₃	81		C3.(He3.S3)	486,25
C₃.₂(He₃.S₃) = (C₃×C₉)⋊C₁₈	central extension (φ=1)	54	6	C3.2(He3.S3)	486,20
C₃.₃(He₃.S₃) = C₃²⋊C₉⋊C₆	central stem extension (φ=1)	18	6	C3.3(He3.S3)	486,6
C₃.₄(He₃.S₃) = C₃²⋊C₉.C₆	central stem extension (φ=1)	54	6	C3.4(He3.S3)	486,10
C₃.₅(He₃.S₃) = C₃²⋊₂D₉.C₃	central stem extension (φ=1)	54	6	C3.5(He3.S3)	486,12

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