A primary goal of precision medicine is to identify patient subgroups based on their characteristics (e.g., comorbidities or genes) with the goal of designing more targeted interventions. While network visualization methods such as Fruchterman-Reingold have been used to successfully identify such patient subgroups in small to medium sized data sets, they often fail to reveal comprehensible visual patterns in large and dense networks despite having significant clustering. We therefore developed an algorithm called ExplodeLayout, which exploits the existence of significant clusters in bipartite networks to automatically "explode" a traditional network layout with the goal of separating overlapping clusters, while at the same time preserving key network topological properties that are critical for the comprehension of patient subgroups. We demonstrate the utility of ExplodeLayout by visualizing a large dataset extracted from Medicare consisting of readmitted hip-fracture patients and their comorbidities, demonstrate its statistically significant improvement over a traditional layout algorithm, and discuss how the resulting network visualization enabled clinicians to infer mechanisms precipitating hospital readmission in specific patient subgroups.