Why does sodium chloride not conduct as much as aluminum chloride in water?

I understand how $\ce{NaCl}$ and $\ce{AlCl3}$ dissolves in water but I'm wondering why one is more conductive than the other. Is it their extra ions to conduct the electricity?


I know that in $\ce{NaCl}$ the water molecules 'steals' the Sodium or the Chloride depending on which end becomes closest to the material due to the Dipole-Dipole attraction. However, this reaction alone cannot break down the ionic lattice alone so there is a separate endothermic reaction. But I still can't understand the science behind why one conducts more than the other.


