Breast cancer is among the most prevalent cancers, and early detection is crucial to successful treatment. One of the most crucial phases of breast cancer treatment is a correct diagnosis. Numerous studies exist about breast cancer classification in the literature. However, analyzing the cancer dataset in the context of clusterability for unsupervised modeling is rare. This work analyzes pointedly the breast cancer dataset clusterability via applying the widely used c-means clustering algorithm and its evolved versions fuzzy and neutrosophic ones. An in-depth comparative study is conducted utilizing a set of quantitative and qualitative clustering efficiency metrics. The study's outcomes divulge the presented neutrosophic c-means clustering superiority in segregating similar breast cancer instances into clusters.