Extensions 1→N→G→Q→1 with N=C₉oHe₃ and Q=C₃

Direct product G=NxQ with N=C₉oHe₃ and Q=C₃

		d	ρ	Label	ID
C₃xC₉oHe₃		81		C3xC9oHe3	243,64

Semidirect products G=N:Q with N=C₉oHe₃ and Q=C₃

extension	φ:Q→Out N	d	ρ	Label	ID
C₉oHe₃:₁C₃ = C₉.He₃	φ: C₃/C₁ → C₃ ⊆ Out C₉oHe₃	27	3	C9oHe3:1C3	243,55
C₉oHe₃:₂C₃ = C₉.₂He₃	φ: C₃/C₁ → C₃ ⊆ Out C₉oHe₃	27	9	C9oHe3:2C3	243,60
C₉oHe₃:₃C₃ = 3_-¹⁺⁴	φ: C₃/C₁ → C₃ ⊆ Out C₉oHe₃	27	9	C9oHe3:3C3	243,66

Non-split extensions G=N.Q with N=C₉oHe₃ and Q=C₃

extension	φ:Q→Out N	d	ρ	Label	ID
C₉oHe₃.₁C₃ = C₉.₅He₃	φ: C₃/C₁ → C₃ ⊆ Out C₉oHe₃	81	3	C9oHe3.1C3	243,19
C₉oHe₃.₂C₃ = C₉.₆He₃	φ: C₃/C₁ → C₃ ⊆ Out C₉oHe₃	81	3	C9oHe3.2C3	243,20
C₉oHe₃.₃C₃ = C₂₇oHe₃	φ: trivial image	81	3	C9oHe3.3C3	243,50

Extensions 1→N→G→Q→1 with N=C9oHe3 and Q=C3