SQL nested aggregate functions MAX(COUNT(*)) - sql

Question

I'm trying to select max(count of rows).
Here is my 2 variants of SELECT
SELECT MAX(COUNT_OF_ENROLEES_BY_SPEC) FROM
(SELECT D.SPECCODE, COUNT(D.ENROLEECODE) AS COUNT_OF_ENROLEES_BY_SPEC
FROM DECLARER D
GROUP BY D.SPECCODE
);
SELECT S.NAME, MAX(D.ENROLEECODE)
FROM SPECIALIZATION S
CROSS JOIN DECLARER D WHERE S.SPECCODE = D.SPECCODE
GROUP BY S.NAME
HAVING MAX(D.ENROLEECODE) =
( SELECT MAX(COUNT_OF_ENROLEES_BY_SPEC) FROM
( SELECT D.SPECCODE, COUNT(D.ENROLEECODE) AS COUNT_OF_ENROLEES_BY_SPEC
FROM DECLARER D
GROUP BY D.SPECCODE
)
);
The first one is working OK, but I want to rewrite it using "HAVING" like in my second variant and add there one more column. But now 2nd variant don't output any data in results, just empty columns.
How can I fix it ? Thank YOU!)

Answer 1

This query based on description given in comments and some suggestions, so it may be wrong:
select -- 4. Join selected codes with specializations
S.Name,
selected_codes.spec_code,
selected_codes.count_of_enrolees_by_spec
from
specialization S,
(
select -- 3. Filter records with maximum popularity only
spec_code,
count_of_enrolees_by_spec
from (
select -- 2. Count maximum popularity in separate column
spec_code,
count_of_enrolees_by_spec,
max(count_of_enrolees_by_spec) over (partition by null) max_count
from (
SELECT -- 1. Get list of declarations and count popularity
D.SPECCODE AS SPEC_CODE,
COUNT(D.ENROLEECODE) AS COUNT_OF_ENROLEES_BY_SPEC
FROM DECLARER D
GROUP BY D.SPECCODE
)
)
where count_of_enrolees_by_spec = max_count
)
selected_codes
where
S.SPECCODE = selected_codes.spec_code
Also query not tested and some syntax errors are possible.