Hi Bryan,
Currently you would need to create multiple groups and create apps that way. Check out this example that the disaster response team has created:
http://www.maps.arcgis.com/apps/MinimalGallery/index.html?appid=b4d43754a17749df81a68838f24d8fba
Each card opens a gallery about a specific topic.
In an upcoming release we are working on adding group categories to a gallery app. This won't allow you to embed groups within groups, but it will allow you to categorize your content, allowing users to select the categories as filters.
Check out the example D in this blog for more information:
https://www.esri.com/arcgis-blog/products/arcgis-online/administration/content-categories-four-ways-...
Let us know if any of these options may help you get up and running.
-Kelly