Deep diffeomorphic registration faces significant challenges for high dimensional images, especially in terms of memory limits. To mitigate this, we propose a Dividing and Downsampling mixed Registration network (DDR-Net), a general architecture that preserves most of image information at multiple scales with reducing memory and inference time cost. In particular, DDR-Net leverages the global context via downsampling the input and utilizes the local details by dividing the input images to subvolumes. Such design fuses global and local information and obtains both coarse-level and fine-level alignments in the final deformation fields. We apply DDR-Net to OASIS dataset. The proposed method is a general method and could be extended to other registration architectures for better performance.