Counting the number of rows in the table - the result of the query SHOW INDEX

Question

Request

SHOW INDEX FROM `table_name` WHERE KEY_NAME = 'index_name'

returns the table. Why can't I display the number of rows in this table with the following query?

 SELECT COUNT(*) FROM (SHOW INDEX FROM `table_name` WHERE KEY_NAME = 'index_name');

Is this a wrong query, or is it basically impossible to print the number of rows in a table - the result of a SHOW INDEX query?

SHOW is not a DML (data management) operator and cannot be used in queries
@Mike, and there is no such command in order to show whether there is an index in the table, and is a DML operator, in MySQL?
Probably the only request is an appeal to the database information_schema? ...

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