Due to space limitations, it is not possible to make the dataset available here on Github. You can access it at: https://www.kaggle.com/zippyz/cats-and-dogs-breeds-classification-oxford-dataset
1 - breeds_classification, where the files referring to the binary classification for cat/dog are found;
2 - species_classification, where the files referring to the categorical classification of breeds can be found (37 in all).
In both cases, the transfer learning technique was used, which imports the pre-trained InceptionV3 network. This one showed a very good performance in both of the proposed problems, not being necessary to apply fine tuning at species_classification.
breeds_classification: 92.78% accuracy (test set)
species_classification: 99.73% accuracy (test set)