I'd heard this anecdotally in the past, apparently there's some meat to it. The Marines have this number set to 3. Marines obviously have different scenarios they have to deal with than most organizations. But it's still an interesting idea. https://www.inc.com/bill-murphy-jr/the-us-marine-corps-uses-...
For firefighters in Germany this is, more or less, defined to be 5.
A group (which is one of the pre-defined tactial units) consists of 9 people: The leader, three troops of two, one machinist, one "Melder" (kind of the guy/girl for "special tasks", helping with whatever is necessary).
The leader commands the troop leaders, machinist and "Melder".
This is expected and taught as the amount of people you can actively manage and take care of in stressful situations like deployments.
edit: for larger deployments you'll have platoon leaders which will command a number of group leaders. for even larger deployments there'll be another layer of command so each platoon leader will only have to lead a set number of group leaders, too.