The fundamental group of the quotient groups

Question

Let $G$ be a simply-connected and connected topological group and let $\Lambda$ be a closed discrete subgroup of $G$. Now, $\pi:G\to G/\Lambda $ is a covering map. What is $\pi_1(G/\Lambda)$? I know it has the same cardinality as $\Lambda$, but is it isomorphic (as groups) to $\Lambda$?