Kindergartens，vacation schools，extracurricular activities，and vocationaleducation and counseling extended the influence ofpublic schools over the lives ofstudents，many of whom in the larger industrial cities were the childrenofimmigrants．
(定语从句many of whom…修饰students)
幼儿园、假期学校、课外活动、职业教育和咨询服务等将公立学校的影响扩大到学生的生活中，而在更大的工业城市中，许多学生都是移民的后代。
分句1：Kindergartens，vacation schools，extracurricular activities，and vocational educationandcounseling extended the influence of public schools over the lives of students
分句2：many of whom in the largerindustrial cities were the children of immigrants
1和2嵌套