Evolutionary game theory has been extensively employed to study the evolution of cooperation in human society. Many previous studies have shown that public cooperation can emerge from positive interactions and social diversity in structured populations. Here we study the evolution of cooperation under N-person interactions, where a minimum threshold of individuals must cooperate to produce public benefits. This is a very common phenomenon in teamwork, especially given the limited capacity of individuals. In this paper, we first present two scenarios of individual contribution mechanisms under an N-person threshold game to characterize such real-world situations. Then, we analyze the stable equilibrium for both scenarios of threshold games in well-mixed populations. Finally, we carry out simulations on three types of complex networks to evaluate the effects of both individual interactions and social diversity on the evolution of cooperation in structured populations. The analytical and simulation results in this paper offer a new insight into the evolution of cooperation in the face of threshold.