Extensions 1→N→G→Q→1 with N=C₄ and Q=C₂²×He₃

Direct product G=N×Q with N=C₄ and Q=C₂²×He₃

		d	ρ	Label	ID
C₂²×C₄×He₃		144		C2^2xC4xHe3	432,401

Semidirect products G=N:Q with N=C₄ and Q=C₂²×He₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄⋊(C₂²×He₃) = C₂×D₄×He₃	φ: C₂²×He₃/C₂×He₃ → C₂ ⊆ Aut C₄	72		C4:(C2^2xHe3)	432,404

Non-split extensions G=N.Q with N=C₄ and Q=C₂²×He₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄.₁(C₂²×He₃) = D₈×He₃	φ: C₂²×He₃/C₂×He₃ → C₂ ⊆ Aut C₄	72	6	C4.1(C2^2xHe3)	432,216
C₄.₂(C₂²×He₃) = SD₁₆×He₃	φ: C₂²×He₃/C₂×He₃ → C₂ ⊆ Aut C₄	72	6	C4.2(C2^2xHe3)	432,219
C₄.₃(C₂²×He₃) = Q₁₆×He₃	φ: C₂²×He₃/C₂×He₃ → C₂ ⊆ Aut C₄	144	6	C4.3(C2^2xHe3)	432,222
C₄.₄(C₂²×He₃) = C₂×Q₈×He₃	φ: C₂²×He₃/C₂×He₃ → C₂ ⊆ Aut C₄	144		C4.4(C2^2xHe3)	432,407
C₄.₅(C₂²×He₃) = C₂×C₈×He₃	central extension (φ=1)	144		C4.5(C2^2xHe3)	432,210
C₄.₆(C₂²×He₃) = M₄(2)×He₃	central extension (φ=1)	72	6	C4.6(C2^2xHe3)	432,213
C₄.₇(C₂²×He₃) = C₄○D₄×He₃	central extension (φ=1)	72	6	C4.7(C2^2xHe3)	432,410

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