Just like SharePoint 2010 it is not possible with SharePoint 2013 to create a view with a ‘group by’ or ‘sort’ for the content type column with the help of the the user interface. Fortunately we can create the ‘group by’ content type view with the help of SharePoint Designer and a bit of code. Sorting the view on content type is not possible with this solution. When using this solution be aware of the following downside. When the view is modified through code, you should no longer edit the view through the user interface. When you edit the view through the user interface the code will be removed automatically.

Solution
1. Create through the user interface the view you need.
2. Set the Group By on the column Created.
3. Save the view.
4. Open the view with SharePoint designer in the advanced mode.
5. Find the following code.

<GroupBy Collapse="TRUE" GroupLimit="30"><FieldRef Name="Created"/></GroupBy>

6. Change Created into ContentType
8. Save the changes.

Result

Inhoudstype is dutch for Contenttype.