I will give you a popular answer. Basically, universities directly under the Ministry of Education belong to the Ministry of Education, and the funds are mainly allocated by the Ministry of Education. The construction of the university is approved by the Ministry of Education, and the president is appointed by the Ministry of Education and is responsible to the Ministry of Education. This is such a concept ~ ~ ~

Directly under the central ministries and commissions, it seems that this is not the exact name, but it can be compared with the Ministry of Education conceptually. I think what you are asking is probably like China Public Security University, which belongs to the Ministry of Public Security, Concord Medical College, Ministry of Health and China Women's College, and belongs to the All-China Women's Federation, but the All-China Women's Federation is not a central ministry ~ ~