You can manage bexio's product groups under "Settings - All settings - Master data - Products: Groups".
To create a new product group, click the "New product group" button. To the right of this you can select the primary product group and then name the new product group under "Name".
You can also create a new product group by opening an existing group and pressing the "+ Create sub-group" button. This will automatically define the open product group as the primary product group.
If you want to delete a product group, left click the desired product group to open it, then press the "Delete" button.