Complex sentence: This process has been opposed by some, perhaps most notably by the Priestly Society of Saint Josaphat which claims to be part of the Ukrainian Greek Catholic Church and which has close links with the Society of St Pius X (SSPX).
Split into simpler sentences: This process has been opposed by some, perhaps most notably within the Ukrainian Greek Catholic Church. The Priestly Society of Saint Josaphat claims to be part of that particular Church, while having close links with the Society of St Pius X (SSPX).