There is not a button to create subfolders, and this must be accomplished using code such as:
os.mkdir("/arcgis/home/newdir")
In the Files pane of an ArcGIS Online Notebook subfolders located within /arcgis/home/ can be selected and a Delete button at the bottom of the pane allows for simple deletion of subfolders.
1) This is not consistent: to have to execute code to create a subfolder, but have a button to delete a subfolder?
2) What other application would you need to run code to create a new item or folder; this is a standard action that should be included in the user interface.
3) If there is a button or menu item to create a subfolder it needs to be improved, as neither I nor Esri Technical Support have located it.