This assignment is made in the project settings. These are defined for the first time when the project is created. They can be changed later (only by project admins) by switching to "Settings" in the project menu.
In the “General” tab, relatively far down, there is the field “Which group does the project belong to? (optional)”.
Important: Here you can only select groups in which the person hiring (i.e. the project admin) is already a member. You may therefore first have to apply for membership in the desired group.
The selection of which projects are assigned to a group is therefore not made by the admins of the group and cannot be directly influenced by them.