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

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

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

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

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃³⋊₁C₆ = C₃³⋊C₆	φ: C₆/C₁ → C₆ ⊆ Aut C₃³	9	6+	C3^3:1C6	162,11
C₃³⋊₂C₆ = C₃×C₃²⋊C₆	φ: C₆/C₁ → C₆ ⊆ Aut C₃³	18	6	C3^3:2C6	162,34
C₃³⋊₃C₆ = S₃×He₃	φ: C₆/C₁ → C₆ ⊆ Aut C₃³	18	6	C3^3:3C6	162,35
C₃³⋊₄C₆ = He₃⋊₄S₃	φ: C₆/C₁ → C₆ ⊆ Aut C₃³	27		C3^3:4C6	162,40
C₃³⋊₅C₆ = C₂×C₃≀C₃	φ: C₆/C₂ → C₃ ⊆ Aut C₃³	18	3	C3^3:5C6	162,28
C₃³⋊₆C₆ = C₆×He₃	φ: C₆/C₂ → C₃ ⊆ Aut C₃³	54		C3^3:6C6	162,48
C₃³⋊₇C₆ = S₃×C₃³	φ: C₆/C₃ → C₂ ⊆ Aut C₃³	54		C3^3:7C6	162,51
C₃³⋊₈C₆ = C₃²×C₃⋊S₃	φ: C₆/C₃ → C₂ ⊆ Aut C₃³	18		C3^3:8C6	162,52
C₃³⋊₉C₆ = C₃×C₃³⋊C₂	φ: C₆/C₃ → C₂ ⊆ Aut C₃³	54		C3^3:9C6	162,53

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

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃³.₁C₆ = C₃²⋊C₁₈	φ: C₆/C₁ → C₆ ⊆ Aut C₃³	18	6	C3^3.1C6	162,4
C₃³.₂C₆ = S₃×3_-¹⁺²	φ: C₆/C₁ → C₆ ⊆ Aut C₃³	18	6	C3^3.2C6	162,37
C₃³.₃C₆ = C₂×C₃²⋊C₉	φ: C₆/C₂ → C₃ ⊆ Aut C₃³	54		C3^3.3C6	162,24
C₃³.₄C₆ = C₆×3_-¹⁺²	φ: C₆/C₂ → C₃ ⊆ Aut C₃³	54		C3^3.4C6	162,49
C₃³.₅C₆ = S₃×C₃×C₉	φ: C₆/C₃ → C₂ ⊆ Aut C₃³	54		C3^3.5C6	162,33
C₃³.₆C₆ = C₉×C₃⋊S₃	φ: C₆/C₃ → C₂ ⊆ Aut C₃³	54		C3^3.6C6	162,39

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