We describe FragGT, a fragment-based evolutionary algorithm for automated molecular design relying on a database of fragments partitioned by gene type, where the gene type of a fragment summarizes the connection types made to adjacent fragments. Organizing fragments by gene type enables trivial mutation between related fragment genes. We demonstrate competitive performance of FragGT on the GuacaMol goal-directed benchmark suite, and show results for FragGTi and Frag-GTic that maintain population diversity using MAP-Elites.