Extensions 1→N→G→Q→1 with N=C₃ and Q=C₃³⋊C₂

Direct product G=N×Q with N=C₃ and Q=C₃³⋊C₂

		d	ρ	Label	ID
C₃×C₃³⋊C₂		54		C3xC3^3:C2	162,53

Semidirect products G=N:Q with N=C₃ and Q=C₃³⋊C₂

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊(C₃³⋊C₂) = C₃⁴⋊C₂	φ: C₃³⋊C₂/C₃³ → C₂ ⊆ Aut C₃	81		C3:(C3^3:C2)	162,54

Non-split extensions G=N.Q with N=C₃ and Q=C₃³⋊C₂

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.(C₃³⋊C₂) = C₃²⋊₄D₉	φ: C₃³⋊C₂/C₃³ → C₂ ⊆ Aut C₃	81		C3.(C3^3:C2)	162,45
C₃.₂(C₃³⋊C₂) = He₃⋊₅S₃	central stem extension (φ=1)	18	6	C3.2(C3^3:C2)	162,46

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=C3 and Q=C33⋊C2