In the Advertising Center you to create custom AdGroups! While creating any Campaign you can assign products to existing AdGroups or create new ones inside the Advertising Center.

To do this, navigate from your Dashboard and open the hamburger menu on the top left to click "Campaigns" under Advertising:

Next, open any campaign and select "Manage Settings", from inside the Campaign Detail page:

While inside the Campaign editor/wizard, on the second step you should find the "Products and AdGroups" page. Assigning AdGroups is simple.
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Choose any product, or products, and assign to a selected AdGroup, or Add to All AdGroups:

To move on to the final Keywords step, click "Next" in the bottom-right hand corner of the screen.

On the last screen of the Campaign editor, you can assign and organize different keywords into specific AdGroups. Once you've finished organizing into AdGroups for your Campaign, click "Finish" to save your changes.
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For more information on Amazon Ad Groups for Sponsored Products, you can read more here.