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We study the cooperative behaviour of the N-person snowdrift game on a square lattice with different neighbourhoods and the cost threshold M for the cooperators.We apply the imitation mechanism for the players and find that there is an optimal frequency of cooperation fC as M varies in the game and the peak of fC shifts to higher M when more neighbours on the lattice are involved in the game.For a given cost-to-benefit ratio r,the system shows discontinuous phase transitions and the behaviour of fC vs M shows step-like structures.We construct payoff level structures and find that the above features can be understood by analyzing the transition behaviour between the payoff levels. The variations of r and M are equivalent to tune the payoff level structures. The plateaus in the step-like structure have similar payoff level structures and the discontinuous jumps correspond to different payoff level structures.