Extensions 1→N→G→Q→1 with N=C₄ and Q=C₂×C₅₄

Direct product G=N×Q with N=C₄ and Q=C₂×C₅₄

		d	ρ	Label	ID
C₂²×C₁₀₈		432		C2^2xC108	432,53

Semidirect products G=N:Q with N=C₄ and Q=C₂×C₅₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄⋊(C₂×C₅₄) = D₄×C₅₄	φ: C₂×C₅₄/C₅₄ → C₂ ⊆ Aut C₄	216		C4:(C2xC54)	432,54

Non-split extensions G=N.Q with N=C₄ and Q=C₂×C₅₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄.₁(C₂×C₅₄) = D₈×C₂₇	φ: C₂×C₅₄/C₅₄ → C₂ ⊆ Aut C₄	216	2	C4.1(C2xC54)	432,25
C₄.₂(C₂×C₅₄) = SD₁₆×C₂₇	φ: C₂×C₅₄/C₅₄ → C₂ ⊆ Aut C₄	216	2	C4.2(C2xC54)	432,26
C₄.₃(C₂×C₅₄) = Q₁₆×C₂₇	φ: C₂×C₅₄/C₅₄ → C₂ ⊆ Aut C₄	432	2	C4.3(C2xC54)	432,27
C₄.₄(C₂×C₅₄) = Q₈×C₅₄	φ: C₂×C₅₄/C₅₄ → C₂ ⊆ Aut C₄	432		C4.4(C2xC54)	432,55
C₄.₅(C₂×C₅₄) = M₄(2)×C₂₇	central extension (φ=1)	216	2	C4.5(C2xC54)	432,24
C₄.₆(C₂×C₅₄) = C₄○D₄×C₂₇	central extension (φ=1)	216	2	C4.6(C2xC54)	432,56

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