How should one call such divisions within the “fragments”?

An answer grounded in the canons cannot be given to such a question, simply because these very “fragments,” i.e. microscopic church jurisdictions existing autonomously, are not provided for in the canons. This should not be forgotten by those who enjoy discoursing loudly about the canons and applying them to our circumstances. The canons present a universal Church made up of united local Churches, along with various divided groups of schismatics, who are outcasts from the Church. In our day, just the opposite is true. What we consider the universal Church is made up of divided “fragments,” which do not associate with each other. Further divisions within the “fragments” can be called “divisions of the church administration.”