How do I cut a git repository in two?

Question

I have a git repository which has several commits into different sub-directories and I want to cut the repository in two in the following way:

/
  sub1/
  sub2/
  sub3/

->

/
  sub1/

The individual subs have evolved to a point where sub1 should be an independent repository. Also there isn't a single commit that touches more than one sub.

So, I'd like to somehow extract a new repository that only takes commits made into sub1 while leaving all other stuff out. But I want to keep the history (but not have the commits related to sub2 nor sub3).

_{Note: I vaguely remember there to be some command to do this, but I never used it myself and don't remember what it was called, so I cannot search for it.}