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

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

		d	ρ	Label	ID
C₄²×He₃		144		C4^2xHe3	432,201

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

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄⋊(C₄×He₃) = C₄⋊C₄×He₃	φ: C₄×He₃/C₂×He₃ → C₂ ⊆ Aut C₄	144		C4:(C4xHe3)	432,207

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

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄.(C₄×He₃) = M₄(2)×He₃	φ: C₄×He₃/C₂×He₃ → C₂ ⊆ Aut C₄	72	6	C4.(C4xHe3)	432,213
C₄.₂(C₄×He₃) = C₁₆×He₃	central extension (φ=1)	144	3	C4.2(C4xHe3)	432,35
C₄.₃(C₄×He₃) = C₂×C₈×He₃	central extension (φ=1)	144		C4.3(C4xHe3)	432,210

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