Fast progress in 3D Gaussian Splatting (3DGS) has made 3D Gaussians popular for 3D modeling and image rendering, but this creates big challenges in data storage and transmission. To obtain a highly compact 3DGS representation, we propose a hybrid entropy model for Gaussian Splatting (HEMGS) data compression, which comprises two primary components, a hyperprior network and an autoregressive network. To effectively reduce structural redundancy across attributes, we apply a progressive coding algorithm to generate hyperprior features, in which we use previously compressed attributes and location as prior information. In particular, to better extract the location features from these compressed attributes, we adopt a domain-aware and instance-aware architecture to respectively capture domain-aware structural relations without additional storage costs and reveal scene-specific features through MLPs. Additionally, to reduce redundancy within each attribute, we leverage relationships between neighboring compressed elements within the attributes through an autoregressive network. Given its unique structure, we propose an adaptive context coding algorithm with flexible receptive fields to effectively capture adjacent compressed elements. Overall, we integrate our HEMGS into an end-to-end optimized 3DGS compression framework and the extensive experimental results on four benchmarks indicate that our method achieves about 40\% average reduction in size while maintaining the rendering quality over our baseline method and achieving state-of-the-art compression results.