select records which do not have a specific flag Oracle

I have a table in this format:

orgkey preferred_flg phonenumber
00111    N          1234566
00111    N          3436456
00111    Y          2388458
00222    N          6634634
00222    N          8834878
00222    N          0034090
00222    N          2736276

I am attempting to get the orgkey which do not have any record with Preferred Flg as Y. For example, from the above sample, I should get 00222 because that orgkey do not have any record with preferred_flg as Y.

I have tried this but it will not give me a count(*) of 0:

select orgkey, count(*)
from phone_table
where preffered_flg != 'Y'
group by orgkey
having count(*) = 0;

Source: oracle

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