Clustering artworks based on style can have many potential real-world applications like art recommendations, style-based search and retrieval, and the study of artistic style evolution of an artist or in an artwork corpus. We introduce and deliberate over the notion of 'Style-based clustering of visual artworks'. We argue that clustering artworks based on style is largely an unaddressed problem. We explore and devise different neural feature representations - from the style-classification, style-transfer to large language vision models - that can be then used for style-based clustering. Our objective is to assess the relative effectiveness of these devised style-based clustering approaches through qualitative and quantitative analysis by applying them to multiple artwork corpora and curated synthetically styled datasets. Besides providing a broad framework for style-based clustering and evaluation, our analysis provides some key novel insights on feature representations, architectures and implications for style-based clustering.