Python Gitlab API - list shared projects of a group/subgroup

I need to find all projects and shared projects within a Gitlab group with subgroups. I managed to list the names of all projects like this:

group = gl.groups.get(11111, lazy=True)

# find all projects, also in subgroups
projects=group.projects.list(include_subgroups=True, all=True)
for prj in projects:
    print(prj.attributes['name'])
print("")

What I am missing is to list also the shared projects within the group. Or maybe to put this in other words: find out all projects where my group is a member. Is this possible with the Python API?

So, inspired by the answer of sytech, I found out that it was not working in the first place, as the shared projects were still hidden in the subgroups. So I came up with the following code that digs through all various levels of subgroups to find all shared projects. I assume this can be written way more elegant, but it works for me:

# group definition
main_group_id = 11111

# create empty list that will contain final result
list_subgroups_id_all = []

# create empty list that act as temporal storage of the results outside the function
list_subgroups_id_stored = []



# function to create a list of subgroups of a group (id)
def find_subgroups(group_id):

    # retrieve group object
    group = gl.groups.get(group_id)

    # create empty lists to store id of subgroups
    list_subgroups_id = []

    #iterate through group to find id of all subgroups
    for sub in group.subgroups.list():
        list_subgroups_id.append(sub.id)

    return(list_subgroups_id)


# function to iterate over the various groups for subgroup detection
def iterate_subgroups(group_id, list_subgroups_id_all):

    # for a given id, find existing subgroups (id) and store them in a list
    list_subgroups_id = find_subgroups(group_id)

    # add the found items to the list storage variable, so that the results are not overwritten
    list_subgroups_id_stored.append(list_subgroups_id)

    # for each found subgroup_id, test if it is already part of the total id list
    # if not, keep store it and test for more subgroups
    for test_id in list_subgroups_id:
        if test_id not in list_subgroups_id_all:

            # add it to total subgroup id list (final results list)
            list_subgroups_id_all.append(test_id)

            # check whether test_id contains more subgroups
            list_subgroups_id_tmp = iterate_subgroups(test_id, list_subgroups_id_all)

            #if so, append to stored subgroup list that is currently checked
            list_subgroups_id_stored.append(list_subgroups_id_tmp)

    return(list_subgroups_id_all)

# find all subgroup and subsubgroups, etc... store ids in list
list_subgroups_id_all = iterate_subgroups(main_group_id , list_subgroups_id_all)

print("***ids of all subgroups***")
print(list_subgroups_id_all)
print("")

print("***names of all subgroups***")
list_names = []
for ids in list_subgroups_id_all:
    group = gl.groups.get(ids)
    group_name = group.attributes['name']
    list_names.append(group_name)
print(list_names)
#print(list_subgroups_name_all)
print("")

# print all directly integrated projects of the main group, also those in subgroups
print("***integrated projects***")
group = gl.groups.get(main_group_id)
projects=group.projects.list(include_subgroups=True, all=True)
for prj in projects:
    print(prj.attributes['name'])
print("")

# print all shared projects
print("***shared projects***")
for sub in list_subgroups_id_all:
    group = gl.groups.get(sub)
    for shared_prj in group.shared_projects:
        print(shared_prj['path_with_namespace'])
print("")

One question that remains - at the very beginning I retrieve the main group by its id (here: 11111), but can I actually also get this id by looking for the name of the group? Something like: group_id = gl.group.get(attribute={'name','foo'}) (not working)?