Symmetries are among of the fundamental properties the Navier-Stokes equations. The large-eddy simulation (LES) equations inherit these symmetries as long as the LES closure respects them. Finding symmetry-preserving LES closures is therefore important to achieve stability and robustness in LES. Classical LES closures based on eddy-viscosity, deconvolution, or scale-similarity preserve many of the original symmetries. Recently, data-driven neural-network closures have been applied in LES to improve accuracy, but stability and generalizability remains a challenge, as symmetries are not automatically enforced. In this work, we compare various approaches to construct symmetry-preserving data-driven LES closures. These include tensor-basis neural networks (TBNNs) and group-convolutional neural-networks. We show that models constrained to respect symmetries are more accurate and stable than identical models without symmetry constraints, while outperforming classical LES closures in both the functional and structural sense.