In recent years, the extraction of overlapping relations has received great attention in the field of natural language processing (NLP). However, most existing approaches treat relational triples in sentences as isolated, without considering the rich semantic correlations implied in the relational hierarchy. Extracting these overlapping relational triples is challenging, given the overlapping types are various and relatively complex. In addition, these approaches do not highlight the semantic information in the sentence from coarse-grained to fine-grained. In this paper, we propose an end-to-end neural framework based on a decomposition model that incorporates multi-granularity relational features for the extraction of overlapping triples. Our approach employs an attention mechanism that combines relational hierarchy information with multiple granularities and pretrained textual representations, where the relational hierarchies are constructed manually or obtained by unsupervised clustering. We found that the different hierarchy construction strategies have little effect on the final extraction results. Experimental results on two public datasets, NYT and WebNLG, show that our mode substantially outperforms the baseline system in extracting overlapping relational triples, especially for long-tailed relations.