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tsql - Find duplicates in SQL

I have a large table with the following data on users.

social security number
name
address

I want to find all possible duplicates in the table where the ssn is equal but the name is not

My attempt is:

SELECT * FROM Table t1
WHERE (SELECT count(*) from Table t2 where t1.name <> t2.name) > 1
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A grouping on SSN should do it

SELECT
   ssn
FROM
   Table t1
GROUP BY
   ssn
HAVING COUNT(*) > 1

..or if you have many rows per ssn and only want to find duplicate names)

...
HAVING COUNT(DISTINCT name) > 1 

Edit, oops, misunderstood

SELECT
   ssn
FROM
   Table t1
GROUP BY
   ssn
HAVING MIN(name) <> MAX(name)

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