Symmetries are among the fundamental properties of physics and partial differential equations [1]. The Navier-Stokes equations are invariant to symmetry groups such as translations, rotations, Galilean transformations, and scaling. These fundamental symmetries are further related to physical properties such as energy-conservation. It is therefore desirable that simplified models and numerical discretizations of the Navier-Stokes equations also respect these symmetries. Symmetry-preserving discretizations have successfully been used for the incompressible Navier-Stokes equations [2]. Large eddy simulation (LES) aims to resolve large scales of turbulent flows only, to reduce the computational cost. This requires choosing a closure model. Recently, deep learning has been used to learn closure models. This requires training data, which is discrete by nature. In a previous work, we showed that discretizing the equations first, before filtering and applying a closure model, removes model-data inconsistencies and improves stability [3]. In this work, we extend this framework with symmetry-preserving neural network closure models. We use group-equivariant steerable neural network layers [4] to enforce symmetries, making the entire discrete LES model physically consistent and stable. We compare the symmetry-preserving closure models to models that are not symmetry-preserving and compare the resulting LES predictions. The symmetry-preserving models achieve the same accuracy with fewer parameters. [1] U. Frisch. Turbulence: the legacy of AN Kolmogorov. Cambridge university press, 1995. [2] R. W. C. P. Verstappen and A. E. P. Veldman. Symmetry-preserving discretization of turbulent flow. J. Comput. Phys., 187(1):343–368, May 2003. [3] S. D. Agdestein and B. Sanderse. Discretize first, filter next: learning divergence-consistent closure models for large-eddy simulation, arXiv: 2403.18088. 2024. [4] M. Weiler and G. Cesa. General E(2)-equivariant steerable CNNs. Advances in Neural Information Processing Systems, volume 32. Curran Associates, Inc., 2019.