Extensions 1→N→G→Q→1 with N=C₃ and Q=C₂₄.S₃

Direct product G=NxQ with N=C₃ and Q=C₂₄.S₃

		d	ρ	Label	ID
C₃xC₂₄.S₃		144		C3xC24.S3	432,230

Semidirect products G=N:Q with N=C₃ and Q=C₂₄.S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃:(C₂₄.S₃) = C₃³:₇C₁₆	φ: C₂₄.S₃/C₃xC₂₄ → C₂ ⊆ Aut C₃	432		C3:(C24.S3)	432,231

Non-split extensions G=N.Q with N=C₃ and Q=C₂₄.S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.(C₂₄.S₃) = C₇₂.S₃	φ: C₂₄.S₃/C₃xC₂₄ → C₂ ⊆ Aut C₃	432		C3.(C24.S3)	432,32
C₃.₂(C₂₄.S₃) = He₃:₄C₁₆	central stem extension (φ=1)	144	3	C3.2(C24.S3)	432,33

Extensions 1→N→G→Q→1 with N=C3 and Q=C24.S3