It's never been explained, but I'm guessing she's just a slight bit below Gil. (I don't think that came out right!
- or maybe in my mind it did :devil
In season 6
Secrets & flies, when she & Sara have the conversation in her office about the ducks (one of my all-time favorite scenes), Cath mentions that she now has to "share this office with the dayshift supervisor". Which, when you think about it, is kind of strange. Gil - the graveshift supervisor - has his own office. Cath, as swing shift supervisor, had her own office then. Now, she has to share with the dayshift supervisor.
That means...first of all, the dayshift supervisor is a woman ("she's got some kind of thing for waterfowl"). Secondly, that dayshift doesn't seem to get much priority if they don't have their own big office like Gil does. Third, Cath still has supervisor duties since she's still got a space as an office.
Also, in the
A la cart episode, Ecklie mentioned to Gil that, because of the "relationship", Cath should have been doing Sara's evaluations - meaning that Cath is still on a higher level than Sara and the other guys.