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In order to implement this you can create a new folder content type and add an order column to this content type. You do need to have the appropriate rights to do so.
The steps would be as follows.
- Go to Site Actions
- Go to Site Settings
- Go to Site Content Types
- Click Create New
- Give it a name such as Folder Order
- Select Parent Content Type from as of Folder Content Types
- Select Folder as the Parent Content Type
- You can create a new group or leave it in custom content types
- Click OK
- At the content type settings click Add from new site column
- Create a site column called Item Order or something similar, select the type as Number
- Click OK
- Go to the list where you want the folders to be ordered
- Go to the list settings
- Go to Advanced Settings
- Select allow management of content types
- Select No for display new folder command on the new menu
- Click OK
- You should now see an area called content types, leave the document as is
- Click Add from existing site content types
- Select the Folder Order (or whatever you named it)
- Click OK
That's it you can now create a folder structure with the order column and order your items as you need.