Extensions 1→N→G→Q→1 with N=C₃ and Q=C₆×D₁₂

Direct product G=N×Q with N=C₃ and Q=C₆×D₁₂

		d	ρ	Label	ID
C₃×C₆×D₁₂		144		C3xC6xD12	432,702

Semidirect products G=N:Q with N=C₃ and Q=C₆×D₁₂

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊₁(C₆×D₁₂) = C₃×S₃×D₁₂	φ: C₆×D₁₂/C₃×D₁₂ → C₂ ⊆ Aut C₃	48	4	C3:1(C6xD12)	432,649
C₃⋊₂(C₆×D₁₂) = C₆×C₁₂⋊S₃	φ: C₆×D₁₂/C₆×C₁₂ → C₂ ⊆ Aut C₃	144		C3:2(C6xD12)	432,712
C₃⋊₃(C₆×D₁₂) = C₆×C₃⋊D₁₂	φ: C₆×D₁₂/S₃×C₂×C₆ → C₂ ⊆ Aut C₃	48		C3:3(C6xD12)	432,656

Non-split extensions G=N.Q with N=C₃ and Q=C₆×D₁₂

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.₁(C₆×D₁₂) = C₆×D₃₆	φ: C₆×D₁₂/C₆×C₁₂ → C₂ ⊆ Aut C₃	144		C3.1(C6xD12)	432,343
C₃.₂(C₆×D₁₂) = C₂×He₃⋊₄D₄	φ: C₆×D₁₂/C₆×C₁₂ → C₂ ⊆ Aut C₃	72		C3.2(C6xD12)	432,350
C₃.₃(C₆×D₁₂) = C₂×D₃₆⋊C₃	φ: C₆×D₁₂/C₆×C₁₂ → C₂ ⊆ Aut C₃	72		C3.3(C6xD12)	432,354
C₃.₄(C₆×D₁₂) = C₁₈×D₁₂	central extension (φ=1)	144		C3.4(C6xD12)	432,346

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