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Cluster analysis of presolar silicon carbide grains based on literature data for 12C/13C, 14N/15N, δ30Si/28Si, and δ29Si/28Si including or not inferred initial 26Al/27Al data, reveals nine clusters agreeing with previously defined grain types but also highlighting new divisions. Mainstream grains reside in three clusters probably representing different parent star metallicities. One of these clusters has a compact core, with a narrow range of composition, pointing to an enhanced production of SiC grains in asymptotic giant branch (AGB) stars with a narrow range of masses and metallicities. The addition of 26Al/27Al data highlights a cluster of mainstream grains, enriched in 15N and 26Al, which cannot be explained by current AGB models. We defined two AB grain clusters, one with 15N and 26Al excesses, and the other with 14N and smaller 26Al excesses, in agreement with recent studies. Their definition does not use the solar N isotopic ratio as a divider, and the contour of the 26Al-rich AB cluster identified in this study is in better agreement with core-collapse supernova models. We also found a cluster with a mixture of putative nova and AB grains, which may have formed in supernova or nova environments. X grains make up two clusters, having either strongly correlated Si isotopic ratios or deviating from the 2/3 slope line in the Si 3-isotope plot. Finally, most Y and Z grains are jointly clustered, suggesting that the previous use of 12C/13C= 100 as a divider for Y grains was arbitrary. Our results show that cluster analysis is a powerful tool to interpret the data in light of stellar evolution and nucleosynthesis modelling and highlight the need of more multi-element isotopic data for better classification.