The lattice $(S(A),\leq)$ of all $L$-valued (fuzzy) subalgebras of the given algebra $A$ is considered. It is proved that for a finite algebra $A$, $(S(A),\leq)$ is isomorphic to a subdirect power of the lattice $L$, if $S(A)$ (the set of ordinary subalgebras of $A$) is closed under unions. Thereby, $(S(A),\leq)$ is distributive if and only if $L$ is distributive. These results are applied to a class of groups.