Extensions 1→N→G→Q→1 with N=C₂² and Q=C₂×C₅₄

Direct product G=N×Q with N=C₂² and Q=C₂×C₅₄

		d	ρ	Label	ID
C₂³×C₅₄		432		C2^3xC54	432,228

Semidirect products G=N:Q with N=C₂² and Q=C₂×C₅₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂²⋊(C₂×C₅₄) = C₂²×C₉.A₄	φ: C₂×C₅₄/C₂×C₁₈ → C₃ ⊆ Aut C₂²	108		C2^2:(C2xC54)	432,225
C₂²⋊₂(C₂×C₅₄) = D₄×C₅₄	φ: C₂×C₅₄/C₅₄ → C₂ ⊆ Aut C₂²	216		C2^2:2(C2xC54)	432,54

Non-split extensions G=N.Q with N=C₂² and Q=C₂×C₅₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂².(C₂×C₅₄) = C₄○D₄×C₂₇	φ: C₂×C₅₄/C₅₄ → C₂ ⊆ Aut C₂²	216	2	C2^2.(C2xC54)	432,56
C₂².₂(C₂×C₅₄) = C₂²⋊C₄×C₂₇	central extension (φ=1)	216		C2^2.2(C2xC54)	432,21
C₂².₃(C₂×C₅₄) = C₄⋊C₄×C₂₇	central extension (φ=1)	432		C2^2.3(C2xC54)	432,22
C₂².₄(C₂×C₅₄) = Q₈×C₅₄	central extension (φ=1)	432		C2^2.4(C2xC54)	432,55

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