${\mathrm{AlCl}}_3$ has a high coordination number. It exists in dimer form and the formula of the dimeric form is ${\mathrm{Al}}_2{\mathrm{Cl}}_6$​. It has vacant  $\mathrm{d}$-orbitals which can absorb electrons from the chlorine atom. It is an electron-deficient compound in $\mathrm{Al}$ (octet incomplete), so it acts as a Lewis acid, and $\mathrm{Al}$ completes it by taking an electron pair from $\mathrm{Cl}$-atoms: