In Android KitKat's 'People' application I was able to access my contacts per group assigned, as shown below using my Nexus 5:
The new 'Contacts' application since the Android Lollipop upgrade does not appear to include this functionality. It's reported to Google in issue #79803 and it appears lots of people are affected by this change.
What is an alternative to this? I'd really like to access my contacts again by their group.