We consider the estimation of a large number of Garch models, of the order of several hundreds. Our interest lies in the identification of common structures in the volatility dynamics of the univariate (or even low-dimensional multivariate) time series. To do so, we classify the series in an unknown number of clusters. Within a cluster, the series share the same model and the same parameters. Each cluster contains therefore similar series. We do not know a priori which series belongs to which cluster. The model is a finite mixture of distributions, where the component weights are unknown parameters and each component distribution has its own conditional mean and variance. Inference is done by the Bayesian approach, using data augmentation techniques. Simulations and an illustration using data on US stocks are provided.