Heterogeneous survival data are commonly present in chronic disease studies. Delineating meaningful disease subtypes directly linked to a survival outcome can generate useful scientific implications. In this work, we develop a latent class proportional hazards (PH) regression framework to address such an interest. We propose mixture proportional hazards modeling, which flexibly accommodates class-specific covariate effects while allowing for the baseline hazard function to vary across latent classes. Adapting the strategy of nonparametric maximum likelihood estimation, we derive an Expectation-Maximization (E-M) algorithm to estimate the proposed model. We establish the theoretical properties of the resulting estimators. Extensive simulation studies are conducted, demonstrating satisfactory finite-sample performance of the proposed method as well as the predictive benefit from accounting for the heterogeneity across latent classes. We further illustrate the practical utility of the proposed method through an application to a mild cognitive impairment (MCI) cohort in the Uniform Data Set.