Fourier neural operators have emerged as data-driven alternatives to conventional numerical simulations for solving partial differential equations. However, these models typically require substantial memory, learnable parameters, and computational resources. In this study, we explore efficient Fourier neural operators through modifications in their width, depth, and cardinality. By leveraging group convolution and channel shuffling, we identified the most effective model for benchmark problems. This model demonstrated a 57\% improvement in prediction accuracy. Our approaches are broadly adaptable to different types of neural operator models.