This grows much more rapidly than either so that even if the utility of groups available to be joined is very small on a per-group basis, eventually the network effect of potential group membership can dominate the overall economics of the system.
However, this includes the (one) empty set, and N singletons, which are not properly subgroups.
From David P. Reed's, "The Law of the Pack" (Harvard Business Review, February 2001, pp 23–4): Reed's Law is often mentioned when explaining competitive dynamics of internet platforms.
As the law states that a network becomes more valuable when people can easily form subgroups to collaborate, while this value increases exponentially with the number of connections, business platform that reaches a sufficient number of members can generate network effects that dominate the overall economics of the system.
According to this argument, the research around Dunbar's number implies a limit on the number of inbound and outbound connections a human in a group-forming network can manage, so that the actual maximum-value structure is much sparser than the set-of-subsets measured by Reed's law or the complete graph measured by Metcalfe's law.