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
C₃×C₃³⋊C₆		18	6	C3xC3^3:C6	486,116

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

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊(C₃³⋊C₆) = C₃⁴⋊₅C₆	φ: C₃³⋊C₆/C₃≀C₃ → C₂ ⊆ Aut C₃	27		C3:(C3^3:C6)	486,167

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

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.(C₃³⋊C₆) = He₃⋊D₉	φ: C₃³⋊C₆/C₃≀C₃ → C₂ ⊆ Aut C₃	81		C3.(C3^3:C6)	486,25
C₃.₂(C₃³⋊C₆) = C₃³⋊₁C₁₈	central extension (φ=1)	18	6	C3.2(C3^3:C6)	486,18
C₃.₃(C₃³⋊C₆) = C₃.C₃≀S₃	central stem extension (φ=1)	54	6	C3.3(C3^3:C6)	486,4
C₃.₄(C₃³⋊C₆) = C₃²⋊C₉⋊S₃	central stem extension (φ=1)	18	6	C3.4(C3^3:C6)	486,7
C₃.₅(C₃³⋊C₆) = (C₃×He₃).C₆	central stem extension (φ=1)	54	6	C3.5(C3^3:C6)	486,9

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