Extensions 1→N→G→Q→1 with N=C₃³ and Q=A₄

Direct product G=N×Q with N=C₃³ and Q=A₄

		d	ρ	Label	ID
A₄×C₃³		108		A4xC3^3	324,171

Semidirect products G=N:Q with N=C₃³ and Q=A₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃³⋊A₄ = C₃³⋊A₄	φ: A₄/C₁ → A₄ ⊆ Aut C₃³	9	4	C3^3:A4	324,160
C₃³⋊₂A₄ = C₃³⋊₂A₄	φ: A₄/C₂² → C₃ ⊆ Aut C₃³	18	3	C3^3:2A4	324,60
C₃³⋊₃A₄ = C₃×C₃²⋊A₄	φ: A₄/C₂² → C₃ ⊆ Aut C₃³	54		C3^3:3A4	324,135

Non-split extensions G=N.Q with N=C₃³ and Q=A₄

extension	φ:Q→Aut N	d	Label	ID
C₃³.₁A₄ = C₆²⋊C₉	φ: A₄/C₂² → C₃ ⊆ Aut C₃³	54	C3^3.1A4	324,59
C₃³.₂A₄ = C₃×C₃².A₄	φ: A₄/C₂² → C₃ ⊆ Aut C₃³	54	C3^3.2A4	324,134
C₃³.₃A₄ = C₃²×C₃.A₄	central extension (φ=1)	162	C3^3.3A4	324,133

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Extensions 1→N→G→Q→1 with N=C33 and Q=A4