Extensions 1→N→G→Q→1 with N=C₃ and Q=C₃×C₄○D₁₂

Direct product G=N×Q with N=C₃ and Q=C₃×C₄○D₁₂

		d	ρ	Label	ID
C₃²×C₄○D₁₂		72		C3^2xC4oD12	432,703

Semidirect products G=N:Q with N=C₃ and Q=C₃×C₄○D₁₂

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊₁(C₃×C₄○D₁₂) = C₃×D₆.₆D₆	φ: C₃×C₄○D₁₂/C₃×Dic₆ → C₂ ⊆ Aut C₃	48	4	C3:1(C3xC4oD12)	432,647
C₃⋊₂(C₃×C₄○D₁₂) = C₃×D₆.D₆	φ: C₃×C₄○D₁₂/S₃×C₁₂ → C₂ ⊆ Aut C₃	48	4	C3:2(C3xC4oD12)	432,646
C₃⋊₃(C₃×C₄○D₁₂) = C₃×D₁₂⋊₅S₃	φ: C₃×C₄○D₁₂/C₃×D₁₂ → C₂ ⊆ Aut C₃	48	4	C3:3(C3xC4oD12)	432,643
C₃⋊₄(C₃×C₄○D₁₂) = C₃×D₆.₃D₆	φ: C₃×C₄○D₁₂/C₃×C₃⋊D₄ → C₂ ⊆ Aut C₃	24	4	C3:4(C3xC4oD12)	432,652
C₃⋊₅(C₃×C₄○D₁₂) = C₃×C₁₂.₅₉D₆	φ: C₃×C₄○D₁₂/C₆×C₁₂ → C₂ ⊆ Aut C₃	72		C3:5(C3xC4oD12)	432,713

Non-split extensions G=N.Q with N=C₃ and Q=C₃×C₄○D₁₂

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.₁(C₃×C₄○D₁₂) = C₃×D₃₆⋊₅C₂	φ: C₃×C₄○D₁₂/C₆×C₁₂ → C₂ ⊆ Aut C₃	72	2	C3.1(C3xC4oD12)	432,344
C₃.₂(C₃×C₄○D₁₂) = C₆².₃₆D₆	φ: C₃×C₄○D₁₂/C₆×C₁₂ → C₂ ⊆ Aut C₃	72	6	C3.2(C3xC4oD12)	432,351
C₃.₃(C₃×C₄○D₁₂) = D₃₆⋊₆C₆	φ: C₃×C₄○D₁₂/C₆×C₁₂ → C₂ ⊆ Aut C₃	72	6	C3.3(C3xC4oD12)	432,355
C₃.₄(C₃×C₄○D₁₂) = C₉×C₄○D₁₂	central extension (φ=1)	72	2	C3.4(C3xC4oD12)	432,347

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁