Extensions 1→N→G→Q→1 with N=C₃ and Q=C₃²xC₄oD₄

Direct product G=NxQ with N=C₃ and Q=C₃²xC₄oD₄

		d	ρ	Label	ID
C₄oD₄xC₃³		216		C4oD4xC3^3	432,733

Semidirect products G=N:Q with N=C₃ and Q=C₃²xC₄oD₄

extension	φ:Q→Aut N	d	Label	ID
C₃:₁(C₃²xC₄oD₄) = C₃²xC₄oD₁₂	φ: C₃²xC₄oD₄/C₆xC₁₂ → C₂ ⊆ Aut C₃	72	C3:1(C3^2xC4oD4)	432,703
C₃:₂(C₃²xC₄oD₄) = C₃²xD₄:₂S₃	φ: C₃²xC₄oD₄/D₄xC₃² → C₂ ⊆ Aut C₃	72	C3:2(C3^2xC4oD4)	432,705
C₃:₃(C₃²xC₄oD₄) = C₃²xQ₈:₃S₃	φ: C₃²xC₄oD₄/Q₈xC₃² → C₂ ⊆ Aut C₃	144	C3:3(C3^2xC4oD4)	432,707

Non-split extensions G=N.Q with N=C₃ and Q=C₃²xC₄oD₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.₁(C₃²xC₄oD₄) = C₄oD₄xC₃xC₉	central extension (φ=1)	216		C3.1(C3^2xC4oD4)	432,409
C₃.₂(C₃²xC₄oD₄) = C₄oD₄xHe₃	central stem extension (φ=1)	72	6	C3.2(C3^2xC4oD4)	432,410
C₃.₃(C₃²xC₄oD₄) = C₄oD₄x3_-¹⁺²	central stem extension (φ=1)	72	6	C3.3(C3^2xC4oD4)	432,411

Extensions 1→N→G→Q→1 with N=C3 and Q=C32xC4oD4