Side-scan sonar (SSS) is a lightweight acoustic sensor that is commonly deployed on autonomous underwater vehicles (AUVs) to provide high-resolution seafloor images. However, leveraging side-scan images for simultaneous localization and mapping (SLAM) presents a notable challenge, primarily due to the difficulty of establishing sufficient amount of accurate correspondences between these images. To address this, we introduce a novel subframe-based dense SLAM framework utilizing side-scan sonar data, enabling effective dense matching in overlapping regions of paired side-scan images. With each image being evenly divided into subframes, we propose a robust estimation pipeline to estimate the relative pose between each paired subframes, by using a good inlier set identified from dense correspondences. These relative poses are then integrated as edge constraints in a factor graph to optimize the AUV pose trajectory. The proposed framework is evaluated on three real datasets collected by a Hugin AUV. Among one of them includes manually-annotated keypoint correspondences as ground truth and is used for evaluation of pose trajectory. We also present a feasible way of evaluating mapping quality against multi-beam echosounder (MBES) data without the influence of pose. Experimental results demonstrate that our approach effectively mitigates drift from the dead-reckoning (DR) system and enables quasi-dense bathymetry reconstruction. An open-source implementation of this work is available.