Extensions 1→N→G→Q→1 with N=C₃ and Q=C₃³×C₆

Direct product G=N×Q with N=C₃ and Q=C₃³×C₆

		d	ρ	Label	ID
C₃⁴×C₆		486		C3^4xC6	486,261

Semidirect products G=N:Q with N=C₃ and Q=C₃³×C₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊(C₃³×C₆) = S₃×C₃⁴	φ: C₃³×C₆/C₃⁴ → C₂ ⊆ Aut C₃	162		C3:(C3^3xC6)	486,256

Non-split extensions G=N.Q with N=C₃ and Q=C₃³×C₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.₁(C₃³×C₆) = C₃×C₆×He₃	central stem extension (φ=1)	162		C3.1(C3^3xC6)	486,251
C₃.₂(C₃³×C₆) = C₃×C₆×3_-¹⁺²	central stem extension (φ=1)	162		C3.2(C3^3xC6)	486,252
C₃.₃(C₃³×C₆) = C₆×C₉○He₃	central stem extension (φ=1)	162		C3.3(C3^3xC6)	486,253
C₃.₄(C₃³×C₆) = C₂×3₊¹⁺⁴	central stem extension (φ=1)	54	9	C3.4(C3^3xC6)	486,254
C₃.₅(C₃³×C₆) = C₂×3_-¹⁺⁴	central stem extension (φ=1)	54	9	C3.5(C3^3xC6)	486,255

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