We recommend to click on the "Active Directory groups" Product Category then you have all available and requestable AD Groups. This shortcut can be used on the start page, on the request overview page and on the request page. Then you can use the Filter Icon on the "Product" column:
Just type the strings you are searching for separated by a blank and choose the option "One or more words".
It will find all AD Groups named "AAA" OR "***"..., for example. As this filters on the collection, it will return results quickly.
If you want to search for a list, you have to customize 'VI_ITShop_AccProductGroupSelector'. Split the string and make an OR statement. Keep in mind, that a lot of ORs will slow down the performance: