This paper studies the implications of punishment-induced conflict in a public goods game. It shows, under plausible assumptions, how larger group size sometimes enhances punishing behavior in social dilemmas and hence supports higher levels of cooperation. Unlike existing approaches that focus on uncoordinated punishment, I consider punishment as a coordinated activity that may be resisted by those being punished and study the implications of punishment-induced conflict situations. Developing a conflict model of punishment and combining it with a standard public good game, I show that coordinated punishment can yield the concentration effect of punishment, leading to a larger group advantage; that is, the larger the group, the easier it becomes to organize cooperation. The key idea is that when punishers coordinate their punishment, punishers as a coalition successfully divide defectors and punish each defector one by one. Surprisingly, even when coordination among punishers decays as group size increases, as long as the rate of decaying remains relatively slow the larger group advantage still obtains.