Face clustering is defined as a technique to group a set of unlabeled faces by visual similarity. While it may seem synonymous with facial recognition, it is different in various aspects. Face recognition is a supervised learning problem, where the facial image dataset along with the class labels are known beforehand. However, face clustering falls under unsupervised classification, as the faces do not have any labels. Such a situation is encountered in numerous real world scenarios, and despite recent advances, implementation of such systems continue to pose a challenge. In this work, we propose a technique to perform face clustering based on piecemeal representations of faces. The purpose is to identify which among the eyes, nose, mouth, or a weighted combination of the three, lead to better performance accuracy. Our method uses four Convolutional Neural Networks, trained from scratch, to extract features from the facial parts acquired from the Georgia Tech face database. Since this face database is labelled, the clustering results can be validated using an external cluster analysis. Moreover, to enhance the clustering procedure, we learn the significance of face parts using genetic algorithms. As a result, the proposed algorithm revealed that some parts of the face are more important than others, at least for the dataset used.