Extensions 1→N→G→Q→1 with N=C₃ and Q=C₃²×C₄○D₄

Direct product G=N×Q with N=C₃ and Q=C₃²×C₄○D₄

		d	ρ	Label	ID
C₄○D₄×C₃³		216		C4oD4xC3^3	432,733

Semidirect products G=N:Q with N=C₃ and Q=C₃²×C₄○D₄

extension	φ:Q→Aut N	d	Label	ID
C₃⋊₁(C₃²×C₄○D₄) = C₃²×C₄○D₁₂	φ: C₃²×C₄○D₄/C₆×C₁₂ → C₂ ⊆ Aut C₃	72	C3:1(C3^2xC4oD4)	432,703
C₃⋊₂(C₃²×C₄○D₄) = C₃²×D₄⋊₂S₃	φ: C₃²×C₄○D₄/D₄×C₃² → C₂ ⊆ Aut C₃	72	C3:2(C3^2xC4oD4)	432,705
C₃⋊₃(C₃²×C₄○D₄) = C₃²×Q₈⋊₃S₃	φ: C₃²×C₄○D₄/Q₈×C₃² → C₂ ⊆ Aut C₃	144	C3:3(C3^2xC4oD4)	432,707

Non-split extensions G=N.Q with N=C₃ and Q=C₃²×C₄○D₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.₁(C₃²×C₄○D₄) = C₄○D₄×C₃×C₉	central extension (φ=1)	216		C3.1(C3^2xC4oD4)	432,409
C₃.₂(C₃²×C₄○D₄) = C₄○D₄×He₃	central stem extension (φ=1)	72	6	C3.2(C3^2xC4oD4)	432,410
C₃.₃(C₃²×C₄○D₄) = C₄○D₄×3_-¹⁺²	central stem extension (φ=1)	72	6	C3.3(C3^2xC4oD4)	432,411

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Extensions 1→N→G→Q→1 with N=C3 and Q=C32×C4○D4