Extensions 1→N→G→Q→1 with N=C₃ and Q=C₆xS₄

Direct product G=NxQ with N=C₃ and Q=C₆xS₄

		d	ρ	Label	ID
C₃xC₆xS₄		54		C3xC6xS4	432,760

Semidirect products G=N:Q with N=C₃ and Q=C₆xS₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃:₁(C₆xS₄) = C₃xS₃xS₄	φ: C₆xS₄/C₃xS₄ → C₂ ⊆ Aut C₃	24	6	C3:1(C6xS4)	432,745
C₃:₂(C₆xS₄) = C₆xC₃:S₄	φ: C₆xS₄/C₆xA₄ → C₂ ⊆ Aut C₃	36	6	C3:2(C6xS4)	432,761

Non-split extensions G=N.Q with N=C₃ and Q=C₆xS₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.₁(C₆xS₄) = C₂xC₃².S₄	φ: C₆xS₄/C₆xA₄ → C₂ ⊆ Aut C₃	18	6+	C3.1(C6xS4)	432,533
C₃.₂(C₆xS₄) = C₆xC₃.S₄	φ: C₆xS₄/C₆xA₄ → C₂ ⊆ Aut C₃	36	6	C3.2(C6xS4)	432,534
C₃.₃(C₆xS₄) = C₂xC₆²:S₃	φ: C₆xS₄/C₆xA₄ → C₂ ⊆ Aut C₃	18	6+	C3.3(C6xS4)	432,535
C₃.₄(C₆xS₄) = C₁₈xS₄	central extension (φ=1)	54	3	C3.4(C6xS4)	432,532

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