The 8th Wonder of the World has got to be why we don't have a native solution to group contact management in iOS. 9 full revisions of this platform later and it's still something overlooked. Luckily, there is a ocean full of 3rd party apps ready to take on the task of being a solution to that oversight. The most recent one to make waves in that ocean is Iteract by Agile Tortoise. You may recognize the developer name because the man behind Interact is also the creator of the brain dump text collection power user app known as Drafts 4.
Interact syncs via iCloud among other services with your contact database. Once synced, you can easily add or remove contacts from groups easily from your iOS device. Need to send a message or email to one of the groups you have set up? There is a composition board where your text rests until your drafts are ready to send off. Another favorite feature of mine is how easy it is to search out contacts and send via the native share sheet. But the best feature? A scratchpad that parses text automatically converting names, companies, phone numbers, emails and addresses allowing you to turn a quick note into a new contact.
There is more to explore. At $4.99, it is a little on the steep side when compared to others that offer some of the same features in the App Store. But the app is Universal, syncs well, has that amazing scratchpad feature and with URL Scheming support, Interact is well worth the asking price.