This paper investigates the impulsive group consensus problems of second-order multi-agent systems under directed network topology with acyclic partition. Two distributed impulsive sampled-data protocols are presented to realise group consensus for both cases with leaders and leaderless, and then some simple yet generic criteria on convergence for such algorithms are established. It is shown that, for the case with leaderless, a feature of the present protocols is to give an explicit expression of group consensus states in terms of the initial values of the agents, which allows us to develop a simple approach yielding the desired group or cluster consensus. While for the case of virtual leaders, a pinning-like tracking technique is effectively designed to regulate all the agents access to the virtual leaders respectively for the purpose of practical control strategy. Finally, simulation results are presented to illustrate the effectiveness of the theoretical analysis.