Eben:
I'm not quite sure if this is exactly what you're asking, but I seem to be able to group layers in ArcGIS Online. I think this might be an issue because most people are uploading single Shapefiles within a Zip file, and then hoping to group them after they have been installed in ArcGIS Online. This cannot be done.
However, if you bundle multiple Shapefiles into one Zip file, and then upload that to ArcGIS Online, the web software will inherently group them together. The only caveat that I can see though is that it only groups the layers in the "Contents" tab, and not the "Legend"...but this I find is Ok because this is where most people will be reading the legend anyway.
ArcGIS Online will name your group based on the name you gave to your Zip file; however, this, of course, can also be edited after you have uploaded the Zip file. I have given you an example of what I have done in the past with ArcGIS Online. The Zip file I just named "Fairview Noise Assessment-July2015", and each Shapefile that was contained in that Zip file is grouped below.
Does this help?