For some reason it seems that you cannot group by the 'Content type' field in SharePoint 2010 lists. This can be solved though by using SharePoint designer. It's not an ideal solution but at least it works.
Open the ASPX page of the view where you want to group by 'Content type'. In there, locate the 'View' XML tag and extend the 'Query' XML to something like this:
Interesting, I was just looking for that.
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