Extensions 1→N→G→Q→1 with N=C₂³ and Q=C₂xHe₃

Direct product G=NxQ with N=C₂³ and Q=C₂xHe₃

		d	ρ	Label	ID
C₂⁴xHe₃		144		C2^4xHe3	432,563

Semidirect products G=N:Q with N=C₂³ and Q=C₂xHe₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂³:(C₂xHe₃) = C₂²xC₃²:A₄	φ: C₂xHe₃/C₃xC₆ → C₃ ⊆ Aut C₂³	36		C2^3:(C2xHe3)	432,550
C₂³:₂(C₂xHe₃) = C₂xD₄xHe₃	φ: C₂xHe₃/He₃ → C₂ ⊆ Aut C₂³	72		C2^3:2(C2xHe3)	432,404

Non-split extensions G=N.Q with N=C₂³ and Q=C₂xHe₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂³.(C₂xHe₃) = C₄xC₃²:A₄	φ: C₂xHe₃/C₃xC₆ → C₃ ⊆ Aut C₂³	36	3	C2^3.(C2xHe3)	432,333
C₂³.₂(C₂xHe₃) = C₂²:C₄xHe₃	φ: C₂xHe₃/He₃ → C₂ ⊆ Aut C₂³	72		C2^3.2(C2xHe3)	432,204
C₂³.₃(C₂xHe₃) = C₂²xC₄xHe₃	central extension (φ=1)	144		C2^3.3(C2xHe3)	432,401

Extensions 1→N→G→Q→1 with N=C23 and Q=C2xHe3