Extensions 1→N→G→Q→1 with N=C₄ and Q=C₂×He₃

Direct product G=N×Q with N=C₄ and Q=C₂×He₃

		d	ρ	Label	ID
C₂×C₄×He₃		72		C2xC4xHe3	216,74

Semidirect products G=N:Q with N=C₄ and Q=C₂×He₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄⋊(C₂×He₃) = D₄×He₃	φ: C₂×He₃/He₃ → C₂ ⊆ Aut C₄	36	6	C4:(C2xHe3)	216,77

Non-split extensions G=N.Q with N=C₄ and Q=C₂×He₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄.(C₂×He₃) = Q₈×He₃	φ: C₂×He₃/He₃ → C₂ ⊆ Aut C₄	72	6	C4.(C2xHe3)	216,80
C₄.₂(C₂×He₃) = C₈×He₃	central extension (φ=1)	72	3	C4.2(C2xHe3)	216,19

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Extensions 1→N→G→Q→1 with N=C4 and Q=C2×He3