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Medical image analysis methods for mammograms, ultrasound, and magnetic resonance imaging (MRI) cannot provide the underline features on the cellular level to understand the cancer microenvironment which makes them unsuitable for breast cancer subtype classification study. In this paper, we propose a convolutional neural network (CNN)-based breast cancer classification method for hematoxylin and eosin (H&E) whole slide images (WSIs). The proposed method incorporates fused mobile inverted bottleneck convolutions (FMB-Conv) and mobile inverted bottleneck convolutions (MBConv) with a dual squeeze and excitation (DSE) network to accurately classify breast cancer tissue into binary (benign and malignant) and eight subtypes using histopathology images. For that, a pre-trained EfficientNetV2 network is used as a backbone with a modified DSE block that combines the spatial and channel-wise squeeze and excitation layers to highlight important low-level and high-level abstract features. Our method outperformed ResNet101, InceptionResNetV2, and EfficientNetV2 networks on the publicly available BreakHis dataset for the binary and multi-class breast cancer classification in terms of precision, recall, and F1-score on multiple magnification levels.