Per this recent paper, individual IQ has no significant correlation with 'group IQ' (defined and measured as the groups ability to accomplish various tasks); group cohesion, motivation, and satisfaction aren't either. The study identified two things that were positively correlated with group IQ: average social sensitivity and a low variance in the amount of time each person spent speaking. (It also found that having more women improved collective intelligence- because women have better social sensitivity.)
(The remaining stuff is idle speculation from me, not the paper. There's no experimental evidence whatsoever backing it up.)
One possible explanation of the contribution of social sensitivity towards collective intelligence is that it reduces conflicts between group members, allowing the group the remain at least somewhat dispassionate/rational about potential solutions instead of turning discussions about solutions into status pissing contests. This is supported by the fact that ego-based actions are well known to be extremely damaging to group outcomes in sports, and that in contexts (e.g. politics) where there are groups with pre-existing conflicts decision-making seems to be relatively poor despite (presumably) higher social sensitivity on the part of politicians. (This also provides an alternative explanation for the benefits of holding off on proposing solutions: while Eliezer focused, as he is wont to do, on the implications for individual rationality, Maier's edict presumably didn't stop people from thinking of potential solutions and privately settling on a preferred solution- but because they hadn't announced it publicly, they would be more willing to listen to others and change their mind.)
The contribution from variance presumably comes from the fact that if people are on average speaking roughly the same amount, then there are more ideas and perspectives being offered than if only a few people dominated the conversation.
I'd also be interested in seeing whether Collective Intelligence is correlated with individual rationality, given that there is little to no correlation between individual rationality and IQ.