The fecal microbiota of ruminants constitutes a diversified community that has been phenotypically associated with a variety of host phenotypes, such as production and health. To gain a better understanding of the complex and interconnected factors that drive the fecal bacterial community, we have aimed to estimate the genetic parameters of the diversity and composition of the fecal microbiota, including heritabilities, genetic correlations among taxa, and genetic correlations between fecal microbiota features and host phenotypes. To achieve this, we analyzed a large population of 1,875 Holstein cows originating from 144 French commercial herds and routinely recorded for production, SCS, and fertility traits. Fecal samples were collected from the animals and subjected to 16S rRNA gene sequencing, with reads classified into amplicon sequence variants (ASV). The estimated α-and β-diversity indices (i.e., Observed Richness, Shannon index, Bray-Curtis and Jaccard dissimilarity matrices) and the abundances of ASV, genera, families, and phyla, normalized by centered-log ratio, were considered as phenotypes. Genetic parameters were calculated using either univariate or bivariate animal models. Heritabilities estimates, ranging from 0.08 to 0.31 for taxa abundances and β-diversity indices, highlight the influence of the host genetics on the composition of the fecal microbiota. Furthermore, genetic correlations estimated within the microbial community and between microbiota features and host traits reveal the complex networks linking all components of the fecal microbiota together and to their host, thus strengthening the holobiont concept. By estimating the heritabilities of microbiota-associated phenotypes, our study quantifies the impact of the host genetics on the fecal microbiota composition. In addition, genetic correlations between taxonomic groups and between taxa abundances and host performance suggest potential applications for selective breeding to improve host traits or promote a healthier microbiota.