No - unless a member in the group shows you or takes a screen shot of the chat and forwards that to non members of the group. Both alternatives are not courteous to the legitimate recipients who may expect privacy.
The way a group text works is like this.
The author of the original group text has a defined list of recipients. The author can choose how the recipients reply to their messages.
A) reply to all members of the group where everyone's reply contributes to the chat or
B) reply back to the original author where only the author can see the replies.
If you are not in the original group of recipients, then no. You can request to be added to the group mid stream but the author or (admin of a chat group like whatsapp) must add you.