Graphical models are a powerful tool for visually representing conditional independence structures of a set of variables. Recently, multiple graphical models for Gaussian variables have been extensively studied to analyse data coming from subgroups or subpopulations. However, proposals for binary sampling models remain limited. Here we present a methodological framework for Bayesian inference and model selection in multiple Ising models. We aim to model the variability introduced into a collection of binary variables due to external factors. The proposed Bayesian approach leverages conjugate priors and Laplace approximations, facilitating efficient model selection through a Metropolis-Hastings algorithm. Our methodological contributions are learning subgroup network structures for both model selection and parameter inference. We compare the performance of our proposed Bayesian method and other competing approaches, and show that our proposed method has a good performance in identifying related groups while offering balanced network sparsity and edge selection.