You put an item into a group from the item itself, not from the group's page. Each item has a Labels field that lists its groups. An item can be in several groups at once.
These lists have a Labels column you can change in place: units, devices, operators, maintenance reminders and SIMs. The steps use the units list.
In the side menu, select Units > List View.
In the unit's row, select the round + pill at the end of its Labels, marked 1.

The labels editor opens with the unit's groups as chips, marked 1, and a list of the account's groups below.

Choose a group from the list, for example Botlek fleet.
The app adds the unit to the group at once. The chip appears in the editor.
Select the close icon at the top right of the editor.
When an item has more groups than the column can show, the pill reads +1, +2 and so on. Select it to see them all.
The add and edit forms of units, devices, operators, maintenance reminders and SIMs have a Labels field. The geofence and route forms call it Label.
The Labels field shows only if your role can read groups.
In the labels editor or the Labels field, enter a name the account does not use yet, for example Night shift.
The list shows the name followed by "(New Label)".

Press Enter.
The app creates the group in the account you are working in and adds the item to it.
If you enter the name of an existing group in other upper and lower case, the app uses the existing group.
Removing an item from a group does not delete the group, even if it becomes empty.
The group's page counts the item under its type. Lists and pickers that work by group, such as the unit list on the map, now include it.
To follow a group on the map, see Track units on the map.