Breast cancer remains a serious global health issue. Leveraging the use of deep learning techniques, this study presents a custom Convolutional Neural Network (CNN) framework for the detection of breast cancer. With the specific objective of accurate classification of breast cancer, a framework is made to analyze high-dimensional medical image information. The CNN's architecture, which consists of specifically developed layers and activation components tailored for the categorization of breast cancer, is described in detail. Utilizing the BreakHis dataset, which comprises biopsy slide images of patients in a range of cancer stages, the model is trained and verified. Comparing our findings to conventional techniques, we find notable gains in sensitivity, specificity, and accuracy. Gray-Level Co-Occurrence Matrix (GLCM) features extracted from the BreakHis dataset was used to analyze the performance on sequential neural network, transfer learning and machine learning models. After analysis, we have proposed hybrid models of CNN-SVM, CNN-KNN, CNN-Logistic regression and achieved accuracy of about 95.2%.