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

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

		d	ρ	Label	ID
C₃²×C₄○D₄		72		C3^2xC4oD4	144,181

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

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊₁(C₃×C₄○D₄) = C₃×C₄○D₁₂	φ: C₃×C₄○D₄/C₂×C₁₂ → C₂ ⊆ Aut C₃	24	2	C3:1(C3xC4oD4)	144,161
C₃⋊₂(C₃×C₄○D₄) = C₃×D₄⋊₂S₃	φ: C₃×C₄○D₄/C₃×D₄ → C₂ ⊆ Aut C₃	24	4	C3:2(C3xC4oD4)	144,163
C₃⋊₃(C₃×C₄○D₄) = C₃×Q₈⋊₃S₃	φ: C₃×C₄○D₄/C₃×Q₈ → C₂ ⊆ Aut C₃	48	4	C3:3(C3xC4oD4)	144,165

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

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.(C₃×C₄○D₄) = C₉×C₄○D₄	central extension (φ=1)	72	2	C3.(C3xC4oD4)	144,50

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