Extensions 1→N→G→Q→1 with N=C₃ and Q=C₂×C₄×A₄

Direct product G=N×Q with N=C₃ and Q=C₂×C₄×A₄

		d	ρ	Label	ID
A₄×C₂×C₁₂		72		A4xC2xC12	288,979

Semidirect products G=N:Q with N=C₃ and Q=C₂×C₄×A₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊₁(C₂×C₄×A₄) = C₄×S₃×A₄	φ: C₂×C₄×A₄/C₄×A₄ → C₂ ⊆ Aut C₃	36	6	C3:1(C2xC4xA4)	288,919
C₃⋊₂(C₂×C₄×A₄) = C₂×Dic₃×A₄	φ: C₂×C₄×A₄/C₂²×A₄ → C₂ ⊆ Aut C₃	72		C3:2(C2xC4xA4)	288,927

Non-split extensions G=N.Q with N=C₃ and Q=C₂×C₄×A₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.(C₂×C₄×A₄) = C₂×C₄×C₃.A₄	central extension (φ=1)	72		C3.(C2xC4xA4)	288,343

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Extensions 1→N→G→Q→1 with N=C3 and Q=C2×C4×A4