The digital age has completely transformed the way that information is processed and stored, which makes cybersecurity a crucial field of research. Cybersecurity contains many different domains, but this work focuses on Intrusion Detection Systems (IDSs). Within the literature, Hierarchical Self-Organizing Maps (HSOMs) have been used to create trustworthy, explainable, and AI-based IDSs. However, HSOMs are trained sequentially, which means that training HSOMs on large datasets is slow. This work presents a novel parallel HSOM architecture, called parHSOM. The purpose of this research is to investigate the effect that parallel computation has on the HSOM training time. parHSOM is tested on two different testbeds, four different output grid sizes, and five different cybersecurity datasets. Performance metrics collected from these experiments show that parHSOM consistently trains faster than the Sequential HSOM algorithm without any significant loss in performance. Additionally, this work provides a platform for further investigation into parallel HSOM implementations.