In oversampled adaptive sensing (OAS), noisy measurements are collected in multiple subframes. The sensing basis in each subframe is adapted according to some posterior information exploited from previous measurements. The framework is shown to significantly outperform the classic non-adaptive compressive sensing approach. This paper extends the notion of OAS to signals with structured sparsity. We develop a low-complexity OAS algorithm based on structured orthogonal sensing. Our investigations depict that the proposed algorithm outperforms the conventional non-adaptive compressive sensing framework with group LASSO recovery via a rather small number of subframes.