Hello,
Thanks for asking. Could you please check out this thread, it looks like it contains a similar question. It would be great if you could leave your comment in there as well. Thanks!
EDIT: There is no subgroup API. Subgroups are groups with Parent_id specified. So to create a Subgroup you use the Group API and specify the Parent_id which is the integer id of the group. The group api group/ will return the first id with that matching name.