Extensions 1→N→G→Q→1 with N=C₃ and Q=C₃²×C₆

Direct product G=N×Q with N=C₃ and Q=C₃²×C₆

		d	ρ	Label	ID
C₃³×C₆		162		C3^3xC6	162,55

Semidirect products G=N:Q with N=C₃ and Q=C₃²×C₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊(C₃²×C₆) = S₃×C₃³	φ: C₃²×C₆/C₃³ → C₂ ⊆ Aut C₃	54		C3:(C3^2xC6)	162,51

Non-split extensions G=N.Q with N=C₃ and Q=C₃²×C₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.₁(C₃²×C₆) = C₆×He₃	central stem extension (φ=1)	54		C3.1(C3^2xC6)	162,48
C₃.₂(C₃²×C₆) = C₆×3_-¹⁺²	central stem extension (φ=1)	54		C3.2(C3^2xC6)	162,49
C₃.₃(C₃²×C₆) = C₂×C₉○He₃	central stem extension (φ=1)	54	3	C3.3(C3^2xC6)	162,50

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Extensions 1→N→G→Q→1 with N=C3 and Q=C32×C6