Extensions 1→N→G→Q→1 with N=C₃³ and Q=C₁₅

Direct product G=N×Q with N=C₃³ and Q=C₁₅

		d	ρ	Label	ID
C₃³×C₁₅		405		C3^3xC15	405,16

Semidirect products G=N:Q with N=C₃³ and Q=C₁₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃³⋊₁C₁₅ = C₅×C₃≀C₃	φ: C₁₅/C₅ → C₃ ⊆ Aut C₃³	45	3	C3^3:1C15	405,7
C₃³⋊₂C₁₅ = C₁₅×He₃	φ: C₁₅/C₅ → C₃ ⊆ Aut C₃³	135		C3^3:2C15	405,12

Non-split extensions G=N.Q with N=C₃³ and Q=C₁₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃³.₁C₁₅ = C₅×C₃²⋊C₉	φ: C₁₅/C₅ → C₃ ⊆ Aut C₃³	135		C3^3.1C15	405,3
C₃³.₂C₁₅ = C₁₅×3_-¹⁺²	φ: C₁₅/C₅ → C₃ ⊆ Aut C₃³	135		C3^3.2C15	405,13

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Extensions 1→N→G→Q→1 with N=C33 and Q=C15