Clustering artworks based on style has many potential real-world applications like art recommendations, style-based search and retrieval, and the study of artistic style evolution in an artwork corpus. However, clustering artworks based on style is largely an unaddressed problem. A few present methods for clustering artworks principally rely on generic image feature representations derived from deep neural networks and do not specifically deal with the artistic style. In this paper, we introduce and deliberate over the notion of style-based clustering of visual artworks. Our main objective is to explore neural feature representations and architectures that can be used for style-based clustering and observe their impact and effectiveness. We develop different methods and assess their relative efficacy for style-based clustering through qualitative and quantitative analysis by applying them to four artwork corpora and four curated synthetically styled datasets. Our analysis provides some key novel insights on architectures, feature representations, and evaluation methods suitable for style-based clustering.