Extensions 1→N→G→Q→1 with N=C₄ and Q=C₃³⋊₅C₄

Direct product G=N×Q with N=C₄ and Q=C₃³⋊₅C₄

		d	ρ	Label	ID
C₄×C₃³⋊₅C₄		432		C4xC3^3:5C4	432,503

Semidirect products G=N:Q with N=C₄ and Q=C₃³⋊₅C₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄⋊(C₃³⋊₅C₄) = C₆².₁₄₇D₆	φ: C₃³⋊₅C₄/C₃²×C₆ → C₂ ⊆ Aut C₄	432		C4:(C3^3:5C4)	432,505

Non-split extensions G=N.Q with N=C₄ and Q=C₃³⋊₅C₄

extension	φ:Q→Aut N	d	Label	ID
C₄.(C₃³⋊₅C₄) = C₃³⋊₁₈M₄(2)	φ: C₃³⋊₅C₄/C₃²×C₆ → C₂ ⊆ Aut C₄	216	C4.(C3^3:5C4)	432,502
C₄.₂(C₃³⋊₅C₄) = C₃³⋊₇C₁₆	central extension (φ=1)	432	C4.2(C3^3:5C4)	432,231
C₄.₃(C₃³⋊₅C₄) = C₂×C₃³⋊₇C₈	central extension (φ=1)	432	C4.3(C3^3:5C4)	432,501

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Extensions 1→N→G→Q→1 with N=C4 and Q=C33⋊5C4