Currently 10 parties in the parliament making up seven fractions. For a supernational parliament the influence of nationalities is generally small, but occasionally it bleeds through.

There's actually more things that you can call parties operating on the European levels but many aren't large/successful enough to be granted party status by the parliament. E.g. Pirates generally fraction with Greens/EFA, Volt is split between Greens/EFA and Renew, roughly left-liberal vs. right-liberal, they really don't seem to be able to decide.