You can only delete major groups that do not have any child records (item groups) assigned. To delete a major group that has item groups, first delete or deactivate the item groups that are assigned to it. Even when it is possible to delete a major group, you are never truly deleting it. Rather, you are setting its status to inactive. Only after a major group is deactivated can you deactivate its over group (its parent).
To deactivate a major group that has no child records: