outlook problems.

I am having a problem with sending group emails.  They go to my send box, but never get to  the people in the group.  I have several groups I email once a week and we upgraded computer and to 365 home and office.  I have been on the phone with my internet provider and they say it is my outlook's fault not theirs, although the first time this happened they said same thing and when I got off with them to contact you I tried to send them out and they went.  I have each group coming to me as well.  I am so frustrated and hope you can help me.