Group convolutional neural networks (G-CNNs) have been shown to increase\nparameter efficiency and model accuracy by incorporating geometric inductive\nbiases. In this work, we investigate the properties of representations learned\nby regular G-CNNs, and show considerable parameter redundancy in group\nconvolution kernels. This finding motivates further weight-tying by sharing\nconvolution kernels over subgroups. To this end, we introduce convolution\nkernels that are separable over the subgroup and channel dimensions. In order\nto obtain equivariance to arbitrary affine Lie groups we provide a continuous\nparameterisation of separable convolution kernels. We evaluate our approach\nacross several vision datasets, and show that our weight sharing leads to\nimproved performance and computational efficiency. In many settings, separable\nG-CNNs outperform their non-separable counterpart, while only using a fraction\nof their training time. In addition, thanks to the increase in computational\nefficiency, we are able to implement G-CNNs equivariant to the\n$\\mathrm{Sim(2)}$ group; the group of dilations, rotations and translations.\n$\\mathrm{Sim(2)}$-equivariance further improves performance on all tasks\nconsidered.\n