Number of levels in the hierarchy seems like a bad way to determine this. I've worked in a company with 500 employees (and three levels) and lots of bureaucracy and a company with 100,000+ employees (~6-8 levels depending on your division) with relatively little bureaucracy (yes, on occasion, I ran in to bad cases of it, but it didn't effect my day-to-day work).
It's simply not possible to have 100,000+ employees and less than 6 levels, unless you have managers with tons of employees. But it is possible to be in a division of a large company where your group has relative autonomy and are empowered to do what they need to do. In my case, there were about 20 of us inside of a larger 500 person group. 95% of decisions were made within the 20 person group (obviously this is an approximation). Another 4% were made at the 500 person group management level. 1% were made by company-wide executives. In other words, my boss was accountable for most of what we did. On occasion, he's need to go to his boss for something. And very rarely, his boss would need to escalate to higher ups (where there were another 3 or 4 levels to the CEO). This company was very well run, but there are much smaller companies with fewer levels in the hierarchy and lots more bureaucracy.
It's simply not possible to have 100,000+ employees and less than 6 levels, unless you have managers with tons of employees. But it is possible to be in a division of a large company where your group has relative autonomy and are empowered to do what they need to do. In my case, there were about 20 of us inside of a larger 500 person group. 95% of decisions were made within the 20 person group (obviously this is an approximation). Another 4% were made at the 500 person group management level. 1% were made by company-wide executives. In other words, my boss was accountable for most of what we did. On occasion, he's need to go to his boss for something. And very rarely, his boss would need to escalate to higher ups (where there were another 3 or 4 levels to the CEO). This company was very well run, but there are much smaller companies with fewer levels in the hierarchy and lots more bureaucracy.