Extensions 1→N→G→Q→1 with N=C₃ and Q=C₆×C₂₄

Direct product G=N×Q with N=C₃ and Q=C₆×C₂₄

		d	ρ	Label	ID
C₃×C₆×C₂₄		432		C3xC6xC24	432,515

Semidirect products G=N:Q with N=C₃ and Q=C₆×C₂₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊₁(C₆×C₂₄) = S₃×C₃×C₂₄	φ: C₆×C₂₄/C₃×C₂₄ → C₂ ⊆ Aut C₃	144		C3:1(C6xC24)	432,464
C₃⋊₂(C₆×C₂₄) = C₃×C₆×C₃⋊C₈	φ: C₆×C₂₄/C₆×C₁₂ → C₂ ⊆ Aut C₃	144		C3:2(C6xC24)	432,469

Non-split extensions G=N.Q with N=C₃ and Q=C₆×C₂₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.₁(C₆×C₂₄) = C₂×C₈×He₃	central stem extension (φ=1)	144		C3.1(C6xC24)	432,210
C₃.₂(C₆×C₂₄) = C₂×C₈×3_-¹⁺²	central stem extension (φ=1)	144		C3.2(C6xC24)	432,211

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Extensions 1→N→G→Q→1 with N=C3 and Q=C6×C24