Extensions 1→N→G→Q→1 with N=C₂³ and Q=He₃:C₂

Direct product G=NxQ with N=C₂³ and Q=He₃:C₂

		d	ρ	Label	ID
C₂³xHe₃:C₂		72		C2^3xHe3:C2	432,561

Semidirect products G=N:Q with N=C₂³ and Q=He₃:C₂

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂³:(He₃:C₂) = C₂xC₃²:S₄	φ: He₃:C₂/C₃² → S₃ ⊆ Aut C₂³	18	3	C2^3:(He3:C2)	432,538
C₂³:₂(He₃:C₂) = C₂xHe₃:₇D₄	φ: He₃:C₂/He₃ → C₂ ⊆ Aut C₂³	72		C2^3:2(He3:C2)	432,399

Non-split extensions G=N.Q with N=C₂³ and Q=He₃:C₂

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂³.(He₃:C₂) = C₆²:₆Dic₃	φ: He₃:C₂/C₃² → S₃ ⊆ Aut C₂³	36	3	C2^3.(He3:C2)	432,260
C₂³.₂(He₃:C₂) = C₆²:₄Dic₃	φ: He₃:C₂/He₃ → C₂ ⊆ Aut C₂³	72		C2^3.2(He3:C2)	432,199
C₂³.₃(He₃:C₂) = C₂²xHe₃:₃C₄	central extension (φ=1)	144		C2^3.3(He3:C2)	432,398

Extensions 1→N→G→Q→1 with N=C23 and Q=He3:C2