Extensions 1→N→G→Q→1 with N=C₃ and Q=C₃²⋊₄D₉

Direct product G=N×Q with N=C₃ and Q=C₃²⋊₄D₉

		d	ρ	Label	ID
C₃×C₃²⋊₄D₉		162		C3xC3^2:4D9	486,240

Semidirect products G=N:Q with N=C₃ and Q=C₃²⋊₄D₉

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊(C₃²⋊₄D₉) = C₃³⋊₉D₉	φ: C₃²⋊₄D₉/C₃²×C₉ → C₂ ⊆ Aut C₃	243		C3:(C3^2:4D9)	486,247

Non-split extensions G=N.Q with N=C₃ and Q=C₃²⋊₄D₉

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.₁(C₃²⋊₄D₉) = C₉²⋊₈S₃	φ: C₃²⋊₄D₉/C₃²×C₉ → C₂ ⊆ Aut C₃	243		C3.1(C3^2:4D9)	486,180
C₃.₂(C₃²⋊₄D₉) = C₃²⋊₄D₂₇	φ: C₃²⋊₄D₉/C₃²×C₉ → C₂ ⊆ Aut C₃	243		C3.2(C3^2:4D9)	486,184
C₃.₃(C₃²⋊₄D₉) = C₃³⋊₆D₉	central stem extension (φ=1)	54		C3.3(C3^2:4D9)	486,181
C₃.₄(C₃²⋊₄D₉) = He₃⋊₄D₉	central stem extension (φ=1)	54	6	C3.4(C3^2:4D9)	486,182

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