Thank you for using Apple Support Communities.
I see that you are having an issue with group messages not working on your iPhone. I would suggest this support article on sending and receiving messages, it has a section on group messages that could help your issue:
If you can‘t send or receive messages on your iPhone, iPad, or iPod touch
If you have issues with a group message
If you’re in a group message and stop receiving messages, check if you left the conversation. Open Messages and tap the group message. If you see the message You left the conversation, then either you left the conversation or you were removed from the group message. You can rejoin a group message only if someone in the group adds you.
You can also start a new group message. Here’s how:
- Open Messages and tap .
- Enter the phone numbers or email addresses of your contacts.
- Write a new message, then tap to send.
If you have other issues with a group message, you might need to delete the conversation and start a new one. To delete a group message:
- Open Messages and find the conversation that you want to delete.
- Swipe left over the conversation.
- Tap Delete.
When you delete a message, you can't recover it. If you want to save parts of a message, take a screenshot. To save an attachment in a message, touch and hold the attachment, tap More, then tap Save.