The transition to electric vehicles is driving a fundamental shift in the automobile design process. Changes in constraints afforded by the absence of a combustion engine create new opportunities for modifying vehicle geometries. Current approaches to optimizing vehicle aerodynamics require a vast amount of computational studies and physical experiments, which are expensive when performing parameter sweeps over conceivable geometric configurations, suggesting the need for more efficient surrogate models to assist analysis. Here we analyze a dataset of industry-quality automobile geometries with their associated aerodynamic performance obtained from experimentally validated, high-fidelity large-eddy simulations. We show that a relationship between these geometries and their respective aerodynamics can be extracted in a low-dimensional manner by leveraging a nonlinear autoencoder which is simultaneously trained to estimate the drag coefficient from the latent variables. We perform aerodynamic design optimization of vehicle designs by making use of the learned aerodynamic relationship in the low-order space obtained by the model. We demonstrate that the aerodynamic trends for the geometries produced from the optimization process show agreement with validation simulations. The findings of this work demonstrate the application of data-driven approaches to the analysis and design of vehicles in a production environment.