  The set of all subracks $\mathcal{R}(X)$ of a finite rack $X$ form a lattice
under inclusion. We prove that if a rack $X$ satisfies a certain condition then
the homotopy type of the order complex of $\mathcal{R}(X)$ is a $(m-2)$-sphere,
where $m$ is the number of maximal subracks of $X$. The rack $X$ satisfying the
condition of this general result is necessarily decomposable. Two particular
instances occur when
  \begin{itemize}
  \item $X=G$ is a group rack, and when
  \item $X=C$ is a conjugacy class rack of a nilpotent group.
  \end{itemize} We also studied the subrack lattices of indecomposable racks by
focusing on the conjugacy class racks of symmetric or alternating groups and
determined the homotopy types of the corresponding order complexes in some
cases.
