Information about the school system in Niedersachsen, also in different languages can be found here: https://www.mk.niedersachsen.de/startseite/schule/unsere_schulen/allgemein_bildende_schulen/
There are state schools in the majority. Some schools are in ecclesiastical sponsorship, but awarded the state-recognized degrees. There are some private schools that charge different levels of school fees (https://www.landesschulbehoerde-niedersachsen.de/themen/schulorganisation/schulen-in-freier-traegerschaft).
In Niedersachsen, there are five types of secondary schools after primary school.
Hauptschule
Hauptschule covers grades 5 to 9. A 10th grade can be set up. The attendance of a 10th grade at Hauptschule is voluntary. Hauptschule gives its pupils a basic general education and an individual vocational orientation. A special focus is on action-based learning. At the end of grade 9, a lower secondary school certificate (Vocational Education Maturity) can be acquired. At the end of class 10, the following qualifications may be obtained: lower secondary school certificate (Vocational Education Maturity), Middle Maturity and a leaving certificate entitling to attend the introductory phase of upper secondary level of Gymnasium. https://www.mk.niedersachsen.de/startseite/schule/unsere_schulen/allgemein_bildende_schulen/hauptschule/hauptschule-6423.html).
Realschule
Realschule includes the grades 5 to 10. It provides their pupils with an extended general education and a general vocational orientation. After the 9th grade, the lower secondary school certificate (Vocational Education Maturity) can be acquired. The following degrees can be obtained at the end of grade 10: lower secondary school certificate (Vocational Education Maturity), Middle Maturity and a leaving certificate entitling to attend the introductory phase of upper secondary school of Gymnasium.
Oberschule
Oberschule covers the grades 5 to 10. By promoting basic skills, self-reliant and social learning, pupils acquire the skills needed to continue their educational career both, professionally and in a study-related manner. The following degrees can be obtained at the end of grade 10: lower secondary school certificate (Vocational Education Maturity), Middle Maturity and a leaving certificate entitling to attend the introductory phase of upper secondary school of Gymnasium.
Gymnasium
Gymnasium covers the grades 5 to 13. Gymnasium gives its pupils a deepened general education and allows the acquisition of the general higher education entrance qualification (Abitur) at the end of class 13. Depending on their achievements, pupils receive at the end of class 10 one of the following degrees: secondary school certificate (Vocational Education Maturity), Middle Maturity or a leaving certificate entitling to attend the introductory phase of upper secondary school of Gymnasium. https://www.mk.niedersachsen.de/startseite/schule/unsere_schulen/allgemein_bildende_schulen/gymnasium/gymnasium-6319.html
Comprehensive school
The comprehensive school covers the classes 5 to 10 or the classes 5 to 13, if the school has an upper secondary level of a Gymnasium. The aim of the comprehensive school is to provide pupils with different learning prerequisites common learning experiences and to promote them individually through differentiated instruction. At comprehensive school, pupils can obtain the same degrees as at Hauptschule, Realschule or Gymnasium.
Information about the vocational schools can be found in the age group 16-18.