Task taxonomies for graph and network visualizations focus on tasks commonly encountered when analyzing graph connectivity and topology. However, in many application fields such as the social sciences (social networks), biology (protein interaction models), software engineering (program call graphs), connectivity and topology information is intertwined with group, clustering, and hierarchical information. Several recent visualization techniques, such as BubbleSets, LineSets and GMap, make explicit use of grouping and clustering, but evaluating such visualization has been difficult due to the lack of standardized group-level tasks. With this in mind, our goal is to define a new set of tasks that assess group-level comprehension. We propose several types of group-level tasks and provide several examples of each type. Finally, we characterize some of the proposed tasks using the multi-level typology of abstract visualization tasks. We believe that adding group-level tasks to the task taxonomy for graph visualization would make the taxonomy more useful for the recent graph visualization techniques. It would help evaluators define and categorize new tasks, and it would help generalize individual results collected in controlled experiments.