Building anthropomorphic robotic and prosthetic hands is a challenging task due to size and performance requirements. As of today it is impossible for such artificial hands to mimic the capabilities of a human hand. A popular approach to reduce the complexity in hand design is the realization of hand synergies through underactuated mechanism, leading also to a reduction of control complexity. In this paper we aim to find grasp synergies of human grasps by employing a deep autoencoder. We perform a grasp study with 15 subjects including 2250 grasps on 35 diverse objects. The emerging latent space contains a comprehensive representation of grasp type and the size of the grasped object, while preserving a large amount of grasp information. In addition we report on novel findings on couplings and grasp specific features of joint kinematics, which can be directly applied to the control of anthropomorphic hands.