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
C₃×C₃²⋊C₆		18	6	C3xC3^2:C6	162,34

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

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊(C₃²⋊C₆) = He₃⋊₄S₃	φ: C₃²⋊C₆/He₃ → C₂ ⊆ Aut C₃	27		C3:(C3^2:C6)	162,40

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) = C₃²⋊D₉	φ: C₃²⋊C₆/He₃ → C₂ ⊆ Aut C₃	27		C3.1(C3^2:C6)	162,5
C₃.₂(C₃²⋊C₆) = C₃³⋊C₆	φ: C₃²⋊C₆/He₃ → C₂ ⊆ Aut C₃	9	6+	C3.2(C3^2:C6)	162,11
C₃.₃(C₃²⋊C₆) = He₃.S₃	φ: C₃²⋊C₆/He₃ → C₂ ⊆ Aut C₃	27	6+	C3.3(C3^2:C6)	162,13
C₃.₄(C₃²⋊C₆) = He₃.₂S₃	φ: C₃²⋊C₆/He₃ → C₂ ⊆ Aut C₃	27	6+	C3.4(C3^2:C6)	162,15
C₃.₅(C₃²⋊C₆) = C₃²⋊C₁₈	central extension (φ=1)	18	6	C3.5(C3^2:C6)	162,4
C₃.₆(C₃²⋊C₆) = C₃≀S₃	central stem extension (φ=1)	9	3	C3.6(C3^2:C6)	162,10
C₃.₇(C₃²⋊C₆) = He₃.C₆	central stem extension (φ=1)	27	3	C3.7(C3^2:C6)	162,12
C₃.₈(C₃²⋊C₆) = He₃.₂C₆	central stem extension (φ=1)	27	3	C3.8(C3^2:C6)	162,14

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