Translation:Her administration is from the same party.
I had a lot of trouble understanding this sentence as a whole, although it was easy to get a correct translation.
"administration" combined with "party" makes me think of government. In that context, I think of "administration" as the total activity of the government, not something that can really be owned by one person. Or, when I do think of "her administration", I think of it as meaning all the government activity that she oversees, and I don't see where being from the same party makes sense.
But now I think that "her administration" must mean "the rest of the government besides her [the leader]".
"by the same party" doesn't really make sense for this sentence. It means that the administration and whatever else you're talking about are from the same political party, in which case "from the same" or "of the same" or "belong to the same" would be the choices, instead of "by the same party" which implies that something was done by that party.