According to the folks who have spent 1000s upon 1000s of hours studying cultures across the world, there are 4 main types of organizational culture:
Collaborative
Creative
Controlled
Competitive
Each of these types of culture lends itself toward flatter or more hierarchical structure, or more internal or external focus as you see here:

Each of these cultural structures has it's own positive and negative traits. Usually a company will have an overarching cultural system, but can have other systems in place in departments or among teams. For example a local city government would typically have an overarching controlled culture, but could have a highly creative department.
Top 5 Collaborative/ Collectivist Traits
Strong personal relationships
Harmony with others
Sense of belonging
Advice seeking
Working as a group
This type of organizational culture is more common in co-operative groups and non-profit organizations. Typically if rewards are given, they are given to all staff rather than top performers. A main focus is on belonging to the group, developing strong relationships within the group, and working with others.
Top 5 Creative / Entrepreneurial Traits
People and empowerment focused
Value creation through innovation and change
Freedom to grow and fail
Commitment and personal responsibility
Emphasis on future and sense of urgency
This type of organizational culture is more common in newer businesses. Those that are establishing themselves is the market value the ability to work quickly, change direction and thrive on encouraging their people to grow and to fail.
Top 5 Controlled / Bureaucratic Traits
Governed by formal rules and standard operating procedures
Clear chain of command
Central decision making
Creates stability
Shared norms guide rewards and punishment
This type of organizational structure is more common in larger businesses and governmental organizations. This kind of structure provides stability, and typically puts minimal pressure on entry level workers. I once worked in a predominantly bureaucratic culture which was difficult for me because I personally prefer predominantly creative cultures. The bureaucratic culture, from my perspective, took too long to adapt to the external changing environment, which was better served by creative counterparts.
Top 5 Competitive / Individualistic Traits
Winning is valued
Members are rewarded for out-performing one another
Focus is on individual achievement
Members operate in a win-lose streak
This type of organizational structure is especially common in sales-driven businesses and departments. I once worked for a sales company that measured every piece of performance data on a daily basis to determine who the highest performers where and who they would cut from their positions performing layoffs on a monthly basis. Needless to say, competitive cultures are typically high stress.
Define Your Tribe: Getting to your Ideal Employee
Culture as one element that helps you to understand who your ideal employee is. Just like I was not a good fit for the Competitive or Bureaucratic cultures, you may interview people who are not a good fit for your culture. This doesn't necessarily mean that they won't be good for you and your company, but you may need to take a different approach with them than your other staff to ensure they want to stick around.
Want to learn more about how you can build systems that support you and your employees? Check out the free Guide to Wholistic Human Resources.