Network Analyst for grouping locations into optimal drive time groups - which one to use?

[MikeBinder]

I'm having trouble figuring how to solve this problem. I did a Origin Destination Cost Matrix, but it didn't product the outcome I was looking for. 

Basically, the goal is to divide 50 points into four groups by choosing the optimal drive time for those 50 locations. Here's a little more detail

• 50 location points across the eastern half of the U.S. (see screenshot) From Lubbock, TX to Boston, MA to Miami, FL to Ames, IA and 46 points in between
• This isn't a warehouse to retail location problem where I'm trying to find the optimal location. All of the point combinations in the groups will be driven. For example when the groups are determined, Point 1 will go to Points 2-13, Point 2 will go to Point 1 and 3-13, etc.   
• Group these 50 points into four groups (two groups of 13, two groups 12) based on the least amount of drive time between each other. Doesn't matter which of the 50 points are grouped together, the only goal is to minimize the overall drive time while creating these four groups 

Using the OD Cost matrix, I'm able to find the 12 or 13 shortest routes from each point, but that's not quite what I'm looking for. 

Any suggestions, ideas, resources on how to solve this problem or go about it? 

[BrittanyBurson]

Also interested in a way to group points based on network location. As an example, we have say 4,000 drains needing inspection across a watershed, but can only get to maybe 40 in a day. So we'd like to group these points into groups of 40 for routing purposes, but from a smarter and network based context... for example, some points are very "near" each other in proximity, but topographically are very distant on the network because one is at the top of a canyon and the other at the bottom, requiring a lot of extra drive time between them. I don't know that we can presently do this with existing network analysis tools, but it would be super helpful.