According to NASA, accidents occurred on 3 of the 22 space flights that carried generators similar to those aboard Galileo.
Literal
American aerospace agency [by-によれば], Galileo-loaded's [and-と] similar generator [object-を] loaded-and went space-flights 22-times [among-のうち], 3-times' flights [in-で] accidents [subject-が] occurred [reported-とのことです].
An extremely complex sentence with multiple embedded clauses. 米航空宇宙局 is NASA. によれば means 'according to.' ガリレオ搭載のものと類似した is a relative clause: 'similar to those aboard Galileo.' ~とのことです is hearsay reporting: 'reportedly/they say that.' Maximum information density.