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

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

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

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

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂²⋊(C₄×He₃) = C₄×C₃²⋊A₄	φ: C₄×He₃/C₃×C₁₂ → C₃ ⊆ Aut C₂²	36	3	C2^2:(C4xHe3)	432,333
C₂²⋊₂(C₄×He₃) = C₂²⋊C₄×He₃	φ: C₄×He₃/C₂×He₃ → C₂ ⊆ Aut C₂²	72		C2^2:2(C4xHe3)	432,204

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

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂².(C₄×He₃) = M₄(2)×He₃	φ: C₄×He₃/C₂×He₃ → C₂ ⊆ Aut C₂²	72	6	C2^2.(C4xHe3)	432,213
C₂².₂(C₄×He₃) = C₂×C₈×He₃	central extension (φ=1)	144		C2^2.2(C4xHe3)	432,210

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