Let \(G\) be a finite group and \(\mathrm{Sp}^n_G=\mathrm{Sp}^n(S^V)\) the spectrum of symmetric products of \(G\)-representation spheres \(S^V\). The author expresses the equivariant rational homotopy groups of this spectrum as the equivariant homology of a subcomplex of the subgroup lattice \(L(G)\) of \(G\). Here \(L(G)\) denotes the simplicial set with \(k\)-simplices given by chains \(H_0 \leq \cdots \leq H_k\) of subgroups of \(G\) and \(L(G)_n\) the subspace of those chains with \([H_k: H_0] \leq n\). The main result is an isomorphism \[ \pi_*^G(\mathrm{Sp}^n_G) \otimes\mathbb{Q} \cong H_*(L(G)_n; \mathbb{Q}))_G. \] The proof is obtained in Schwede’s global equivariant context [S. Schwede, Global homotopy theory. Cambridge: Cambridge University Press (2018; Zbl 1451.55001)]. Several sample calculations are given for groups \(G\) of small order.