When I worked at 3M as a senior engineer, I embarked on an exercise to see just how far into the company I was.  I was surprised to learn that there were 7 layers of managers between me and the CEO.  I had my supervisor who did my performance evaluations.  I had my manager whom I interacted with occasionally in department meetings.  After those 2 layers, I had few interactions with the division manager, the division director, the division president, the business unit president or the executive VP that connected me to the CEO.  At the time, 3M had 60,000 employees.
As someone who has studied organizations for a long time, I’ve found when you get above 500 employees, the organization starts to shift from an organization to more of an ecosystem.  Many of you probably live in a town of less than 60K people.  Running an organization of that size is more like governing a community than it is running a company.  While there are common characteristics within any company of that size, there are a lot more cultural differences as you go between teams, departments, divisions, and business units than there are similarities. 
However, because when we study business, we tend to talk about the bigger companies, I think we come to the wrong conclusions.  I know a lot of business owners and executive leaders who are proud to proclaim how they run a “flat organizational structure”.  This often means that managers have large numbers of direct reports.  This is especially true in healthcare where I’ve seen managers with as many as 25,50,60,80 or in one case, 160 direct report employees.
It’s important I pause and define a “direct report”.  A direct report is someone who reports directly to you and not to someone else.  If you are a manager and you have 5 supervisors with 60 employees, you don’t have 60 direct reports.  You have 5 direct reports, which is reasonable. 
But we often see organizations who have managers who directly oversee dozens of employees and the impact is devastating to the organization.  Trying to run a “flat organization” doesn’t reduce hierarchy, especially if your employees have almost no chance of getting time with their supervisor.  We know from Gallup that 70% of disengagement is caused by management and one of the leading causes of disengagement is a poor or non-existent relationship between the manager and their employee.  
At one hospital, a department where a single manager oversaw 80 direct reports learned that 25% of their employees considered themselves to be toxic.  We installed 5 supervisors between the manager and the employees and, within a year, the toxicity dropped to 8%.  This reduced turnover in the department and improved quality.
I am often asked about the “right number” of direct reports.  There is no hard number where a team will suddenly break down but we look at a few factors.  If every employee on the team does the same or similar job at the same time, then you can have more employees (maybe up to 15).  If the jobs are more complex and unique from each other, then managers should really have no more than 8 employees.  
A lot of organizations create “lead” positions to help managers out, but we warn companies that this is always a great solution.  Giving one of your best employees a “lead” position where they are responsible for the performance of people on their team without any authority is a great way to burn out your best people.  Leads are truly effective IF the people below them really do report to them and they have authority as a manager. 
Take a look throughout your organization.  If you have an area where a manager oversees more than 15 direct reports, you probably have an opportunity to increase engagement, reduce turnover, and reduce the risk of burning out your best people.