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Breast cancer is a significant cause of cancer-related mortality among women around the globe, underscoring the need for early and accurate diagnosis. Typically, histopathological analysis of biopsy slides is utilized for tumor classification. However, it is labor-intensive, subjective, and often affected by inter-observer variability. Therefore, this study explores a deep learning-based, multi-class classification framework for distinguishing breast cancer subtypes using Convolutional Neural Networks (CNNs). Unlike previous work done on the popular BreakHis dataset, where binary classification models are applied, in this work, we differentiate eight histopathological subtypes, four benign (adenosis, fibroadenoma, phyllodes tumor, tubular adenoma) and four malignant (ductal carcinoma, lobular carcinoma, mucinous carcinoma, papillary carcinoma). This work leverages transfer learning with ImageNet-pretrained ResNet architectures (ResNet-18, ResNet-34, and ResNet-50) and extensive data augmentation to enhance classification accuracy and robustness across magnifications. Among all the ResNet models, ResNet-50 achieved the best performance, attaining a maximum accuracy of 92.30%, an AUC-ROC of 99.79%, and an average specificity of 98.61%. These findings validate the combined effectiveness of CNNs and transfer learning in capturing fine-grained histopathological features required for accurate breast cancer subtype classification.