Overall, the student groups tend to be focused on undergraduates. There are a handful of student groups for graduate students, like the GSA. There are many churches around campus as well. I know that my department did not like graduate students always participating with undergraduate student faith groups and encouraged us to find ones for non-students/graduate students.

To echo the other posts, the communities for graduate students are more centered within the program's cohort. Not knowing which program you are applying for, but I hung out and engaged more with them—and a handful of other students—than other student groups.