Modern machine learning models are prone to over-reliance on spurious correlations, which can often lead to poor performance on minority groups. In this paper, we identify surprising and nuanced behavior of finetuned models on worst-group accuracy via comprehensive experiments on four well-established benchmarks across vision and language tasks. We first show that the commonly used approach of class-balanced mini-batch finetuning can induce a decrease in worst-group accuracy (WGA) with training epochs, leading to performance no better than without class-balancing. While in some scenarios, removing data to create a class-balanced subset is more effective, we show this depends on group structure and propose a mixture method which can outperform both techniques. Next, we show that scaling pretrained models is generally beneficial for worst-group accuracy, but only in conjuction with appropriate class-balancing. Finally, we identify spectral imbalance in finetuning features as a potential source of group disparities --- minority group covariances incur a larger spectral norm than majority groups once conditioned on the classes. Our results show more nuanced interactions of modern finetuned models with group robustness than was previously known.