This dependent clause is a participle carrying
NP, (which is) derived from the nonrestrictive relative clause (which was) carrying
NP. Relative clauses modify nouns; this one modifies the noun phrase the plane, and therefore should come immediately after it.
There are several different kinds of subordinate clauses:
some (complement clauses) have to go either before, or more often after, verbs,
some (adverb clauses) can go in a number of places, and
some (relative clauses like this, which are adjective clauses) have to go after the nouns they modify.
Just saying "subordinate clause" doesn't give enough information here.