Create a new git repo out of only a sub-directory of an existing repo

gistfile1.sh

# clone the original repo
git clone git@github.com:user/repo.git
cd ./repo

# filter all git history (including all branches) and only keep the commits affecting a given subdirectory
git filter-branch --subdirectory-filter the/sub/dir -- --all

# clean up git backups (only necessary to help making sure all that we don't want is gone afterwards):
git for-each-ref --format="%(refname)" refs/original/ | xargs -n 1 git update-ref -d
git reflog expire --expire=now --all
git gc --prune=now
# we can now check that the history looks fine if we want to

# now push to a new repo:
git remote add new-repo git@github.com:user/new-repo.git
# push everything:
git push new-repo refs/remotes/origin/*:refs/heads/*