Back when I used to DM regularly, I would NEVER split up the party. If I left some of my players alone for five minutes, conversations would erupt and I could never get them to focus on the game again.
That can definitely be a problem. That's why in the scenario that I set up, we'll be doing a single round of group 1, followed by a single round of group 2, and then group 3, and then back to group 1; regardless of whether a given group is in combat or not. It gives everyone at the table a reason to not start side conversations when your group's turn is going to come up shortly and is not much different than an entire round of normal initiative.