Actually, I'm told that the Catholic Church is 242 contradictory denominations, and that figure comes from a reliable, Catholic-vetted source!
From the source you listed:
“From these western and smaller eastern rites the encyclopedia gets 242 “Roman Catholic denominations” (year 2000 numbers). The largest is by far the Latin-rite (commonly called “Roman Catholics” by non-Catholic Christians) with 976 million members of the 994 million total members (or 98% of the total, year 1995 numbers). However, since virtually all of these western and smaller eastern rites are in union with the Pope (I am not sure of some of them), there is actually one
Catholic Church, not 242 churches or denominations. Based on the encyclopedia’s own definition of “denomination” the editors appear to be separating and counting by country which is how you get to 242 (or 238 countries plus 4) “denominations” of Roman Catholics. The Catholic Church in Canada is not a different “denomination” from the Catholic Church in the U.S., which is not a different Catholic Church from the one in England, etc. If you search the available “World Christian Database” online, there is indeed one Catholic Church in the U.S.A., (see also Barrett, Encyclopedia, volume 1, page 783 for the U.S.A.) and in the world there are indeed 238 “Roman Catholic” denominations (for exactly 238 countries), i.e. one Catholic Church for each country. The same “counting by country” seems to be the case with some of the denominations in the other mega-blocs.
When dividing these “denominations” by country as they do, there are definitely some problems in figuring out the true total
“denominations” since many of them are being counted more than once — and in fact 241 times too much in the case of “Roman Catholic” denominations. Barrett’s Encyclopedia states this explicitly:
“As a statistical unit in this Encyclopedia, a ‘denomination’ always refers to one single country. Thus the Roman Catholic Church, although a single organization, is described here as consisting of 236 denominations in the world’s 238 countries”
And several of them even have their own Popes.
Those are rites, not "contradictory denominations."