Also, it look like device settings are set differently. On my phone, the settings show I have SMS delivery enabled, which means "Notifications are OFF" But on the computer, I have the opposite. On my phone, if I turn SMS off, then it gives me some options, and at the bottom it says "Not receiving notifications? Try turning them on and off. Double check they are enabled in the settings app" and then has a link to my PHONE's settings for GroupMe and an option to reset them.
I have to say, between group settings and device settings, this is really confusing.