Local Climate Zones (LCZs) give a zoning map to study urban structures and land use and analyze the impact of urbanization on local climate. Multimodal remote sensing enables LCZ classification, for which data fusion is significant for improving accuracy owing to the data complexity. However, there is a gap in a comprehensive analysis of the fusion mechanisms used in their deep learning (DL) classifier architectures. This study analyzes different fusion strategies in the multi-class LCZ classification models for multimodal data and grouping strategies based on inherent data characteristics. The different models involving Convolutional Neural Networks (CNNs) include: (i) baseline hybrid fusion (FM1), (ii) with self- and cross-attention mechanisms (FM2), (iii) with the multi-scale Gaussian filtered images (FM3), and (iv) weighted decision-level fusion (FM4). Ablation experiments are conducted to study the pixel-, feature-, and decision-level fusion effects in the model performance. Grouping strategies include band grouping (BG) within the data modalities and label merging (LM) in the ground truth. Our analysis is exclusively done on the So2Sat LCZ42 dataset, which consists of Synthetic Aperture Radar (SAR) and Multispectral Imaging (MSI) image pairs. Our results show that FM1 consistently outperforms simple fusion methods. FM1 with BG and LM is found to be the most effective approach among all fusion strategies, giving an overall accuracy of 76.6\%. Importantly, our study highlights the effect of these strategies in improving prediction accuracy for the underrepresented classes. Our code and processed datasets are available at https://github.com/GVCL/LCZC-MultiModalHybridFusion