A maximal chain of a finite lattice is called smooth if any two intervals of the same length are isomorphic. We say that a group \(G\) is a smooth group (respectively, a totally smooth group) if its subgroup lattice \(L(G)\) possesses a smooth chain (respectively, all maximal chains in \(L(G)\) are smooth).
The main goal of this paper is to determine all finite totally smooth groups. According to Theorem 1, these are the cyclic groups of prime power order, the \(P\)-groups and the cyclic groups of square free order. There are also described the finite groups for which all maximal subgroups are totally smooth (Theorem 2).