Populate nested json from mysql

Question

I am trying to use the full calendar scheduler plugin and I am trying to create the required JSON from my database. The format needed is shown below. I need to the staff do be "children" of their department

So all the cleaners would show under cleaning, human resources under human resources etc

   [
        {
            id: '1',
            title: 'Cleaning',
            children: [
                {
                    id: '2',
                    title: 'Cleaner 1'
                },
                {
                    id: '2',
                    title: 'Cleaner 2'
                }
            ]
        },
{
            id: '2',
            title: 'Human Resources',
            children: [
                {
                    id: '2',
                    title: 'Human resources 1'
                },
                {
                    id: '2',
                    title: 'Human resources 2'
                }
            ]
        }
    ]

My tables are shown below:

Groups table:
ID | GROUP_NAME
1  | Human Resources
2  | Cleaning
3  | Warehouse

Staff table
ID | GROUP_ID | STAFF_NAME
1  | 1        | Human resources 1
2  | 1        | Human resources 2
3  | 2        | Cleaning 1
4  | 2        | Cleaning 2
5  | 3        | Warehouse 1

My code so far, it just outputs everything

$data = array();

$getgroups = mysqli_query($con, "SELECT groups.id, groups.group_name, person.name, person.id AS personid FROM groups INNER JOIN interns ON groups.id = interns.group_id");

while($group = mysqli_fetch_assoc($getgroups)) {

    $data[] = array(
        "id" => $group["id"], //Group ID
        "title" => $group["group_name"], //Group Name
        "children" => array([
            "id" => $group["id"],
            "title" => $group["personid"], //Intern name
            ])
    );
}

echo json_encode($data);