Extensions 1→N→G→Q→1 with N=C₃ and Q=C₂⁴⋊₄S₃

Direct product G=N×Q with N=C₃ and Q=C₂⁴⋊₄S₃

		d	ρ	Label	ID
C₃×C₂⁴⋊₄S₃		24		C3xC2^4:4S3	288,724

Semidirect products G=N:Q with N=C₃ and Q=C₂⁴⋊₄S₃

extension	φ:Q→Aut N	d	Label	ID
C₃⋊₁(C₂⁴⋊₄S₃) = C₆²⋊₅D₄	φ: C₂⁴⋊₄S₃/C₆.D₄ → C₂ ⊆ Aut C₃	48	C3:1(C2^4:4S3)	288,625
C₃⋊₂(C₂⁴⋊₄S₃) = C₆²⋊₄D₄	φ: C₂⁴⋊₄S₃/C₂×C₃⋊D₄ → C₂ ⊆ Aut C₃	48	C3:2(C2^4:4S3)	288,624
C₃⋊₃(C₂⁴⋊₄S₃) = C₆²⋊₂₄D₄	φ: C₂⁴⋊₄S₃/C₂³×C₆ → C₂ ⊆ Aut C₃	72	C3:3(C2^4:4S3)	288,810

Non-split extensions G=N.Q with N=C₃ and Q=C₂⁴⋊₄S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.(C₂⁴⋊₄S₃) = C₂⁴⋊₄D₉	φ: C₂⁴⋊₄S₃/C₂³×C₆ → C₂ ⊆ Aut C₃	72		C3.(C2^4:4S3)	288,163

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Extensions 1→N→G→Q→1 with N=C3 and Q=C24⋊4S3