Given a group size m and a sensitive dataset D, group privacy (GP) releases information about D with the guarantee that the adversary cannot infer with high confidence whether the underlying data is D or a neighboring dataset D' that differs from D by m records. GP generalizes the well-established notion of differential privacy (DP) for protecting individuals' privacy; in particular, when m=1, GP reduces to DP. Compared to DP, GP is capable of protecting the sensitive aggregate information of a group of up to m individuals, e.g., the average annual income among members of a yacht club. Despite its longstanding presence in the research literature and its promising applications, GP is often treated as an afterthought, with most approaches first developing a DP mechanism and then using a generic conversion to adapt it for GP, treating the DP solution as a black box. As we point out in the paper, this methodology is suboptimal when the underlying DP solution involves subsampling, e.g., in the classic DP-SGD method for training deep learning models. In this case, the DP-to-GP conversion is overly pessimistic in its analysis, leading to low utility in the published results under GP. Motivated by this, we propose a novel analysis framework that provides tight privacy accounting for subsampled GP mechanisms. Instead of converting a black-box DP mechanism to GP, our solution carefully analyzes and utilizes the inherent randomness in subsampled mechanisms, leading to a substantially improved bound on the privacy loss with respect to GP. The proposed solution applies to a wide variety of foundational mechanisms with subsampling. Extensive experiments with real datasets demonstrate that compared to the baseline convert-from-blackbox-DP approach, our GP mechanisms achieve noise reductions of over an order of magnitude in several practical settings, including deep neural network training.