Every org will differ, as will names of roles, expectation of roles, expectations for the number of levels, etc... The following will help visualze a hypothetical org on the order of 60-200 people.
IC: Individual Contributor
IC with Reports: A composite role mixing some IC work with some Management
Manager: A supervisor for ICs and ICs with Reports
Manager of Managers / Director : A supervisor whose reports include a Manager
Director / VP: A supervisor whose reports include a Manager of Managers
Building a balanced Org is like building a balanced tree. In the canvas below is a random org structure statisfying the specified configuration.
As a thought exercise: begin with the default org below and continue to increment ICs until the org no longer works. Then start promoting ICs to IC with reports, or promote ICs with reports to managers, and org balance can be restored, allowing for continued hiring...