Analysis
NAICS 92311 is the 2022 NAICS industry for administration of education programs, part of 9231 (Administration of Human Resource Programs).
It has only one more detailed code, 923110, which covers exactly the same activities; the definition, index entries and statistics are on that page.
County Business Patterns excludes public administration, so there is no establishment count for it.
Official definition
See industry description for 923110.
Source: US Census Bureau, NAICS 2022 Manual.