You can browse all branches before cloning at https://github.com/ILIAS-eLearning/ILIAS (Drop down list on first tab)
A single branch is cloned into the current directory (which must be empty for that to work !) by:
git clone --single-branch -b BRANCHNAME https://github.com/ILIAS-eLearning/ILIAS.git .
i.e. for Branch "release_6":
git clone --single-branch -b release_6 https://github.com/ILIAS-eLearning/ILIAS.git .