Finger vein identification has become a promising biometric modality due to its anti-spoofing capability, time-invariant nature, privacy and security when compared to other predominant biometric traits. In the wake of the recent epidemics and pandemics, the world has recognized the need for hygienic and contactless identification techniques such as finger vein. Although finger vein biometrics has been around for some time, there doesn't exist any classification scheme for finger vein images similar to the Henry classes for fingerprints. For large scale biometric identification systems, an accurate and consistent classification mechanism can significantly reduce the search space and time for matching. In this paper, we first show that finger vein patterns can be classified into four classes namely, Fork, Eye, Bridge and Arch (FEBA) and then propose an identification scheme based on this classification. To the best of our knowledge, this is the first-ever attempt on classifying finger vein images based on intrinsic anatomical features. We obtained a classification accuracy of 95.88% using convolutional neural network and an average reduction of 86.89% in matching time on a heterogeneous database consisting of 4 different datasets. Cross dataset validation and comparison with existing algorithms have been performed to show the efficacy of the proposed classification and matching mechanism.