The capsids of double-stranded DNA viruses protect the viral genome from the harsh extracellular environment, while maintaining stability against the high internal pressure of packaged DNA. To elucidate how capsids maintain stability in an extreme environment, we used cryoelectron microscopy to determine the capsid structure of the thermostable phage P74-26. We find the P74-26 capsid exhibits an overall architecture that is very similar to those of other tailed bacteriophages, allowing us to directly compare structures to derive the structural basis for enhanced stability. Our structure reveals lasso-like interactions that appear to function like catch bonds. This architecture allows the capsid to expand during genome packaging, yet maintain structural stability. The P74-26 capsid has T=7 geometry despite being twice as large as mesophilic homologs. Capsid capacity is increased through a novel mechanism with a larger, flatter major capsid protein. Our results suggest that decreased icosahedral complexity (i.e. lower T number) leads to a more stable capsid assembly.