Extensions 1→N→G→Q→1 with N=C₂² and Q=C₂²×He₃

Direct product G=N×Q with N=C₂² and Q=C₂²×He₃

		d	ρ	Label	ID
C₂⁴×He₃		144		C2^4xHe3	432,563

Semidirect products G=N:Q with N=C₂² and Q=C₂²×He₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂²⋊(C₂²×He₃) = C₂²×C₃²⋊A₄	φ: C₂²×He₃/C₆² → C₃ ⊆ Aut C₂²	36		C2^2:(C2^2xHe3)	432,550
C₂²⋊₂(C₂²×He₃) = C₂×D₄×He₃	φ: C₂²×He₃/C₂×He₃ → C₂ ⊆ Aut C₂²	72		C2^2:2(C2^2xHe3)	432,404

Non-split extensions G=N.Q with N=C₂² and Q=C₂²×He₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂².(C₂²×He₃) = C₄○D₄×He₃	φ: C₂²×He₃/C₂×He₃ → C₂ ⊆ Aut C₂²	72	6	C2^2.(C2^2xHe3)	432,410
C₂².₂(C₂²×He₃) = C₄²×He₃	central extension (φ=1)	144		C2^2.2(C2^2xHe3)	432,201
C₂².₃(C₂²×He₃) = C₂²⋊C₄×He₃	central extension (φ=1)	72		C2^2.3(C2^2xHe3)	432,204
C₂².₄(C₂²×He₃) = C₄⋊C₄×He₃	central extension (φ=1)	144		C2^2.4(C2^2xHe3)	432,207
C₂².₅(C₂²×He₃) = C₂²×C₄×He₃	central extension (φ=1)	144		C2^2.5(C2^2xHe3)	432,401
C₂².₆(C₂²×He₃) = C₂×Q₈×He₃	central extension (φ=1)	144		C2^2.6(C2^2xHe3)	432,407

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