WHEN Yitta Schwartz died last month at 93, she left behind 15 children, more than 200 grandchildren and so many great- and great-great-grandchildren that, by her family’s count, she could claim perhaps 2,000 living descendants.

Mrs. Schwartz was a member of the Satmar Hasidic sect, whose couples have nine children on average and whose ranks of descendants can multiply exponentially. But even among Satmars, the size of Mrs. Schwartz’s family is astonishing. A round-faced woman with a high-voltage smile, she may have generated one of the largest clans of any survivor of the Holocaust — a thumb in the eye of the Nazis.

Her descendants range in age from a 75-year-old daughter named Shaindel to a great-great-granddaughter born Feb. 10 named Yitta in honor of Mrs. Schwartz and a great-great-grandson born Feb. 15 who was named Moshe at his circumcision on Monday. Their numbers include rabbis, teachers, merchants, plumbers and truck drivers. But these many apples have not fallen far from the tree: With a few exceptions, like one grandson who lives in England, they mostly live in local Satmar communities, like Williamsburg in Brooklyn and Kiryas Joel, near Monroe, N.Y., where Mrs. Schwartz lived for the last 30 years of her life.

Mrs. Schwartz had a zest for life and a devotion to Hasidic rituals, faithfully attending the circumcisions, first haircuts, bar mitzvahs, engagements and weddings of her descendants. With 2,000 people in the family, such events occupied much of the year.