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

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

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

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

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₃³×C₆)⋊₁C₃ = C₂×C₃²⋊He₃	φ: C₃/C₁ → C₃ ⊆ Aut C₃³×C₆	54		(C3^3xC6):1C3	486,196
(C₃³×C₆)⋊₂C₃ = C₆×C₃≀C₃	φ: C₃/C₁ → C₃ ⊆ Aut C₃³×C₆	54		(C3^3xC6):2C3	486,210
(C₃³×C₆)⋊₃C₃ = C₃×C₆×He₃	φ: C₃/C₁ → C₃ ⊆ Aut C₃³×C₆	162		(C3^3xC6):3C3	486,251

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

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₃³×C₆).₁C₃ = C₂×C₃³⋊C₉	φ: C₃/C₁ → C₃ ⊆ Aut C₃³×C₆	54		(C3^3xC6).1C3	486,73
(C₃³×C₆).₂C₃ = C₆×C₃²⋊C₉	φ: C₃/C₁ → C₃ ⊆ Aut C₃³×C₆	162		(C3^3xC6).2C3	486,191
(C₃³×C₆).₃C₃ = C₂×C₃⁴.C₃	φ: C₃/C₁ → C₃ ⊆ Aut C₃³×C₆	54		(C3^3xC6).3C3	486,197
(C₃³×C₆).₄C₃ = C₃×C₆×3_-¹⁺²	φ: C₃/C₁ → C₃ ⊆ Aut C₃³×C₆	162		(C3^3xC6).4C3	486,252

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