Extensions 1→N→G→Q→1 with N=C₂³ and Q=C₃²:C₆

Direct product G=NxQ with N=C₂³ and Q=C₃²:C₆

		d	ρ	Label	ID
C₂³xC₃²:C₆		72		C2^3xC3^2:C6	432,558

Semidirect products G=N:Q with N=C₂³ and Q=C₃²:C₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂³:(C₃²:C₆) = C₂xC₆²:S₃	φ: C₃²:C₆/C₃² → S₃ ⊆ Aut C₂³	18	6+	C2^3:(C3^2:C6)	432,535
C₂³:₂(C₃²:C₆) = C₂xC₆²:C₆	φ: C₃²:C₆/C₃:S₃ → C₃ ⊆ Aut C₂³	18	6+	C2^3:2(C3^2:C6)	432,542
C₂³:₃(C₃²:C₆) = C₂xHe₃:₆D₄	φ: C₃²:C₆/He₃ → C₂ ⊆ Aut C₂³	72		C2^3:3(C3^2:C6)	432,377

Non-split extensions G=N.Q with N=C₂³ and Q=C₃²:C₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂³.(C₃²:C₆) = C₆²:₅Dic₃	φ: C₃²:C₆/C₃² → S₃ ⊆ Aut C₂³	36	6-	C2^3.(C3^2:C6)	432,251
C₂³.₂(C₃²:C₆) = C₆²:₄C₁₂	φ: C₃²:C₆/C₃:S₃ → C₃ ⊆ Aut C₂³	36	6-	C2^3.2(C3^2:C6)	432,272
C₂³.₃(C₃²:C₆) = C₆²:₃C₁₂	φ: C₃²:C₆/He₃ → C₂ ⊆ Aut C₂³	72		C2^3.3(C3^2:C6)	432,166
C₂³.₄(C₃²:C₆) = C₂²xC₃²:C₁₂	central extension (φ=1)	144		C2^3.4(C3^2:C6)	432,376

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