Excessively large classes that encapsulate multiple responsibilities are challenging to comprehend and maintain. Addressing this issue, several Extract Class refactoring tools have been proposed, employing a two-phase process: identifying suitable fields or methods for extraction, and implementing the mechanics of refactoring. These tools traditionally generate an intra-class dependency graph to analyze the class structure, applying hard-coded rules based on this graph to unearth refactoring opportunities. Yet, the graph-based approach predominantly illuminates direct, \textit{one-to-one}'' relationship between pairwise entities. Such a perspective is restrictive as it overlooks the complex,\textit{one-to-many}'' dependencies among multiple entities that are prevalent in real-world classes. This narrow focus can lead to refactoring suggestions that may diverge from developers' actual needs, given their multifaceted nature. To bridge this gap, our paper leverages the concept of intra-class dependency hypergraph to model \textit{one-to-many} dependency relationship and proposes a hypergraph learning-based approach to suggest Extract Class refactoring opportunities named HECS. For each target class, we first construct its intra-class dependency hypergraph and assign attributes to nodes with a pre-trained code model. All the attributed hypergraphs are fed into an enhanced hypergraph neural network for training. Utilizing this trained neural network alongside a large language model (LLM), we construct a refactoring suggestion system. We trained HECS on a large-scale dataset and evaluated it on two real-world datasets. The results show that demonstrates an increase of 38.5% in precision, 9.7% in recall, and 44.4% in f1-measure compared to 3 state-of-the-art refactoring tools including JDeodorant, SSECS, and LLMRefactor, which is more useful for 64% of participants. The results also unveil practical suggestions and new insights that benefit existing extract-related refactoring techniques.