Extensions 1→N→G→Q→1 with N=C₃ and Q=C₆×C₄○D₄

Direct product G=N×Q with N=C₃ and Q=C₆×C₄○D₄

		d	ρ	Label	ID
C₄○D₄×C₃×C₆		144		C4oD4xC3xC6	288,1021

Semidirect products G=N:Q with N=C₃ and Q=C₆×C₄○D₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊₁(C₆×C₄○D₄) = C₆×C₄○D₁₂	φ: C₆×C₄○D₄/C₂²×C₁₂ → C₂ ⊆ Aut C₃	48		C3:1(C6xC4oD4)	288,991
C₃⋊₂(C₆×C₄○D₄) = C₆×D₄⋊₂S₃	φ: C₆×C₄○D₄/C₆×D₄ → C₂ ⊆ Aut C₃	48		C3:2(C6xC4oD4)	288,993
C₃⋊₃(C₆×C₄○D₄) = C₆×Q₈⋊₃S₃	φ: C₆×C₄○D₄/C₆×Q₈ → C₂ ⊆ Aut C₃	96		C3:3(C6xC4oD4)	288,996
C₃⋊₄(C₆×C₄○D₄) = C₃×S₃×C₄○D₄	φ: C₆×C₄○D₄/C₃×C₄○D₄ → C₂ ⊆ Aut C₃	48	4	C3:4(C6xC4oD4)	288,998

Non-split extensions G=N.Q with N=C₃ and Q=C₆×C₄○D₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.(C₆×C₄○D₄) = C₄○D₄×C₁₈	central extension (φ=1)	144		C3.(C6xC4oD4)	288,370

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