We experimentally demonstrate group synchrony in a network of four nonlinear optoelectronic oscillators with time-delayed coupling. We divide the nodes into two groups of two each, by giving each group different parameters and by enabling only intergroup coupling. When coupled in this fashion, the two groups display different dynamics, with no isochronal synchrony between them, but the nodes in a single group are isochronally synchronized, even though there is no intragroup coupling. We compare experimental behavior with theoretical and numerical results.