An exhibition opening next week at the Museum of the City of New York will trace New York Catholics’ growth from a small religious minority to a politically powerful group with a wide range of institutions spanning the five boroughs.

“Catholics in New York, 1808-1946” — organized in light of the Archdiocese of New York’s bicentennial celebration — makes its debut on May 16. The exhibit is organized around three key themes: the centrality of parish life, the evolution of church-run schools, hospitals, and social welfare organizations, and the rise of Catholics as a major force in city politics.

The beginning date of the exhibition, 1808, was when New York had enough Catholics to be named a diocese. A diocese gets a bishop; a bishopric gets a cathedral. The New York diocese began building its first cathedral in 1809, at Mott and Prince streets. It opened in 1815. The French-born architect Joseph François Mangin, whose earlier credits included the Louis XV-style City Hall, startlingly chose a Gothic style for the cathedral at a time when the Gothic Revival had mostly to do with eccentric private houses and garden follies, and had not yet become the titanic force in church design that it would be 20 years later. (Mangin’s design was compromised following an 1860s fire and rebuilding of the cathedral.)

New York Catholics achieved diocesan mass in 1808, but they’d been around for a while. The first Catholic priest in the New Netherland colony was the French missionary Isaac Jogues, later killed by upstate Iroquois. In 1664, the colony passed to the Catholic James, Duke of York. He named Thomas Dongan, a Catholic, as Colonial governor. The “Dongan Charter,” establishing religious freedom in the colony, foreshadows the Constitution and Bill of Rights. Alas for James: England’s Glorious Revolution deposed him in 1688. The new monarchs were the Protestants William and Mary. Between 1688 and 1783, New York colony forbade the practice of the Catholic faith.

Even with independence, there were those who believed Catholics should have to renounce their faith to become citizens — the old “dual allegiance” (to America and to Rome) thing. Nonetheless, the Bill of Rights enshrined religious freedom, and New York’s first Catholic parish — St. Peter’s, formed in 1783 — built its first church in 1786. The present St. Peter’s, on Barclay and Church streets, is the congregation’s second home, completed in 1840. The community life of Catholic parishes, beginning with St. Peter’s, will be a major theme of the exhibition.

Irish immigration swelled New York’s Catholic population. Great numbers of Irish came to New York well prior to the famine migrations of the 1840s and 1850s, and labored on great public-works projects, such as the Erie Canal and the Croton water system. That these Irish often undercut native-born workingmen in the labor market, and besides which practiced a strange, inscrutable religion, led to gang violence such as that portrayed in Martin Scorsese’s 2002 film “Gangs of New York.” The forthcoming exhibit will look at how this “community of immigrants” faced down prevalent anti-Catholic sentiment. Indeed, the most visually arresting part of Mangin’s old St. Patrick’s Cathedral is the high, sinuously buckling brick wall surrounding the property. The wall served a defensive purpose, as nativist gangs often vandalized Catholic churches.

That said, the famine migrations of the Irish utterly transformed New York, where the 1855 census showed nearly one-third of all city residents to be Irish born. The same years saw mass immigration of Germans, many of whom were also Catholic, though the Irish had firm control of what in 1850 had become an archdiocese.

The greatest figure of New York’s 19th-century church was John Hughes, an Irish immigrant and the city’s first archbishop. Hughes oversaw a ferociously growing, desperately poor flock. He built churches, orphanages, hospitals, and schools, creating the basic institutional structure that New York’s church possesses to this day. The Museum of the City of New York show will give plentiful space to the building of institutions, including the parochial school system, St. Vincent’s Hospital, and the New York Foundling Hospital. Hughes also ordered construction of a new cathedral on Fifth Avenue at 50th Street, an edifice that, by being the city’s most splendid, would assert that New York had — like it or not — become a Catholic city. Hughes laid the cornerstone in 1858, but died 15 years before the cathedral’s 1879 opening.

At the end of the 19th century, new Catholic immigrants — Italians, Poles, and others — arrived. The different national groups worshipped in their own ways, with their own special devotions and saints. A given Catholic parish was largely an Irish one, or a German one, or an Italian one. In the 1880s, Italian Catholics built the Church of St. Anthony of Padua, on Sullivan Street just south of Houston Street. The Italians used the Romanesque style of the 13th-century Basilica of San Francesco in Assisi, feeling that the Irish had monopolized Gothic.

A high point in the history of New York’s churches came between 1919 and 1938, the episcopate of Patrick Hayes. The city’s Catholics by then were considered — and considered themselves — New Yorkers and Americans, and had overcome the manifold hardships of the immigrant years. Catholic seminaries had to turn away aspiring priests. Cardinal Hayes himself, a child of the Five Points (once New York’s most notorious slum), earned all New Yorkers’ admiration.

One focus of the Museum of the City of New York exhibition will be Catholics in New York politics. By the end of World War II, Irish Catholics had dominated New York City’s Democratic Party for 75 years, and Italian Catholics, who earlier in the century had shunned politics, were a rising force (and remain one to this day).

The show takes museumgoers through 1946, a time when large numbers of immigrant Catholic families were making use of government programs, such as the G.I. Bill — providing education and vocational training, and loans to World War II veterans — and were beginning to move out of the city.

Fordham University Press has published a companion book for the show, “Catholics in New York: Society, Culture, and Politics, 1808-1946,” edited by Terry Golway and featuring essays by Pete Hamill, Tyler Anbinder, William Donohue, and others. Topics include the Italian influence on Catholic New York, Cardinal Spellman and New York’s Puerto Ricans, and the city’s Polish Catholics.

The story on tap at the Museum of the City of New York is nothing less than the story of New York itself.

Until December 31 (1220 Fifth Ave. at 103rd, 212-534-1672)