We propose assessing a mixture model in a cluster analysis setting with the inegrated classification likelihood. With this purpose, the observed data are assigned to unknown clusters using a maximum a posteriori operator. The integrated completed likelihood approximation is derived without the theoretical difficulties encountered when approximating the integrated observed likelihood. Numerical experiments on simulated and real data of the resulting ICL criterion show that it performs well both for choosing a mixture model and a relevant number of clusters. In particular, ICL appears to be more robust than BIC to violation of some of the mixture model assumptions and it can select a number of clusters leading to a sensible partitioning of the data.