Three-dimensional (3D) medical image classification is useful in applications such as disease diagnosis and content-based medical image retrieval. It is a challenging task due to several reasons. First, image intensity values are vastly different depending on the image modality. Second, intensity values within the same image modality may vary depending on the imaging machine and artifacts may also be introduced in the imaging process. Third, processing 3D data requires high computational power. In recent years, significant research has been conducted in the field of 3D medical image classification. However, most of these make assumptions about patient orientation and imaging direction to simplify the problem and/or work with the full 3D images. As such, they perform poorly when these assumptions are not met. In this paper, we propose a method of classification for 3D organ images that is rotation and translation invariant. To this end, we extract a representative two-dimensional (2D) slice along the plane of best symmetry from the 3D image. We then use this slice to represent the 3D image and use a 20-layer deep convolutional neural network (DCNN) to perform the classification task. We show experimentally, using multi-modal data, that our method is comparable to existing methods when the assumptions of patient orientation and viewing direction are met. Notably, it shows similarly high accuracy even when these assumptions are violated, where other methods fail. We also explore how this method can be used with other DCNN models as well as conventional classification approaches.