Extensions 1→N→G→Q→1 with N=C₃ and Q=C₂³.₁₄D₆

Direct product G=N×Q with N=C₃ and Q=C₂³.₁₄D₆

		d	ρ	Label	ID
C₃×C₂³.₁₄D₆		48		C3xC2^3.14D6	288,710

Semidirect products G=N:Q with N=C₃ and Q=C₂³.₁₄D₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊₁(C₂³.₁₄D₆) = Dic₃⋊D₁₂	φ: C₂³.₁₄D₆/Dic₃⋊C₄ → C₂ ⊆ Aut C₃	48		C3:1(C2^3.14D6)	288,534
C₃⋊₂(C₂³.₁₄D₆) = C₆².₅₅C₂³	φ: C₂³.₁₄D₆/D₆⋊C₄ → C₂ ⊆ Aut C₃	96		C3:2(C2^3.14D6)	288,533
C₃⋊₃(C₂³.₁₄D₆) = C₆².₁₁₃C₂³	φ: C₂³.₁₄D₆/C₆.D₄ → C₂ ⊆ Aut C₃	48		C3:3(C2^3.14D6)	288,619
C₃⋊₄(C₂³.₁₄D₆) = C₆²⋊₆D₄	φ: C₂³.₁₄D₆/C₂²×Dic₃ → C₂ ⊆ Aut C₃	48		C3:4(C2^3.14D6)	288,626
C₃⋊₅(C₂³.₁₄D₆) = C₆².₁₁₂C₂³	φ: C₂³.₁₄D₆/C₂×C₃⋊D₄ → C₂ ⊆ Aut C₃	48		C3:5(C2^3.14D6)	288,618
C₃⋊₆(C₂³.₁₄D₆) = C₆²⋊₇D₄	φ: C₂³.₁₄D₆/C₂×C₃⋊D₄ → C₂ ⊆ Aut C₃	48		C3:6(C2^3.14D6)	288,628
C₃⋊₇(C₂³.₁₄D₆) = C₆²⋊₁₄D₄	φ: C₂³.₁₄D₆/C₆×D₄ → C₂ ⊆ Aut C₃	144		C3:7(C2^3.14D6)	288,796

Non-split extensions G=N.Q with N=C₃ and Q=C₂³.₁₄D₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.(C₂³.₁₄D₆) = Dic₉⋊D₄	φ: C₂³.₁₄D₆/C₆×D₄ → C₂ ⊆ Aut C₃	144		C3.(C2^3.14D6)	288,149

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁