Extensions 1→N→G→Q→1 with N=C₂³ and Q=C₃:Dic₃

Direct product G=NxQ with N=C₂³ and Q=C₃:Dic₃

		d	ρ	Label	ID
C₂³xC₃:Dic₃		288		C2^3xC3:Dic3	288,1016

Semidirect products G=N:Q with N=C₂³ and Q=C₃:Dic₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂³:(C₃:Dic₃) = C₂xC₆.₇S₄	φ: C₃:Dic₃/C₆ → S₃ ⊆ Aut C₂³	72		C2^3:(C3:Dic3)	288,916
C₂³:₂(C₃:Dic₃) = C₆².₃₈D₄	φ: C₃:Dic₃/C₃² → C₄ ⊆ Aut C₂³	72		C2^3:2(C3:Dic3)	288,309
C₂³:₃(C₃:Dic₃) = C₂xC₆²:₅C₄	φ: C₃:Dic₃/C₃xC₆ → C₂ ⊆ Aut C₂³	144		C2^3:3(C3:Dic3)	288,809

Non-split extensions G=N.Q with N=C₂³ and Q=C₃:Dic₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂³.(C₃:Dic₃) = C₁₂.₁₂S₄	φ: C₃:Dic₃/C₆ → S₃ ⊆ Aut C₂³	72	6	C2^3.(C3:Dic3)	288,402
C₂³.₂(C₃:Dic₃) = (C₆xD₄).S₃	φ: C₃:Dic₃/C₃² → C₄ ⊆ Aut C₂³	72		C2^3.2(C3:Dic3)	288,308
C₂³.₃(C₃:Dic₃) = C₆²:₇C₈	φ: C₃:Dic₃/C₃xC₆ → C₂ ⊆ Aut C₂³	144		C2^3.3(C3:Dic3)	288,305
C₂³.₄(C₃:Dic₃) = C₂xC₁₂.₅₈D₆	φ: C₃:Dic₃/C₃xC₆ → C₂ ⊆ Aut C₂³	144		C2^3.4(C3:Dic3)	288,778
C₂³.₅(C₃:Dic₃) = C₂²xC₃²:₄C₈	central extension (φ=1)	288		C2^3.5(C3:Dic3)	288,777

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