Slow Query time with Function in Group By

Question

I have a PL/SQL function that computes status based on several inputs. When the function is run in a standard query without a group by, it is very fast. When i try to count or sum other columns in the select (thus requiring the Group By), my query response time explodes exponentially.
My query:
SELECT
ben.atm_class( 'DBT', 'CLA' , 6 , 1245 ),
count (distinct ax.HOUSEHOLD_KEY)
FROM
ADM.PRODUCT p,
ADM.ACCOUNT_CROSS_FUNCTIONAL ax
WHERE
ax.month_key = 1245
AND ( ax.PRODUCT_KEY=ADM.P.PRODUCT_KEY )
AND ( ax.HOUSEHOLD_KEY ) IN (6)
group by
p.ptype, p.stype,
ben.atm_class( 'DBT', 'CLA' , 6 , 1245 )
My explain plan for the query with the Group By:
Operation     Object Name     Rows     Bytes     Cost     Object Node     In/Out     PStart     PStop
SELECT STATEMENT Optimizer Mode=CHOOSE          3           10                     
SORT GROUP BY          3      60      10                     
NESTED LOOPS          3      60      6                     
TABLE ACCESS BY LOCAL INDEX ROWID     ACCOUNT_CROSS_FUNCTIONAL     3      33      3                23     23
INDEX RANGE SCAN     NXIF312ACCOUNT_CROSS_FUNCTION     3           2                23     23
TABLE ACCESS BY INDEX ROWID     PRODUCT     867      7 K     1                     
INDEX UNIQUE SCAN     PK_PRODUCT_PRODUCTKEY     867                               
This executes in over 9 minutes.
My query w/o Group by
SELECT
ben.atm_class( 'DBT', 'CLA' , 6 , 1245 ),
ax.HOUSEHOLD_KEY
FROM
ADM.PRODUCT p,
ADM.ACCOUNT_CROSS_FUNCTIONAL ax
WHERE
ax.month_key = 1245
AND ( ax.PRODUCT_KEY=ADM.P.PRODUCT_KEY )
AND ( ax.HOUSEHOLD_KEY ) IN (6)
My explain plan without the Group By:
Operation     Object Name     Rows     Bytes     Cost     Object Node     In/Out     PStart     PStop
SELECT STATEMENT Optimizer Mode=CHOOSE          3           3                     
NESTED LOOPS          3      42      3                     
TABLE ACCESS BY LOCAL INDEX ROWID     ACCOUNT_CROSS_FUNCTIONAL     3      33      3                23     23
INDEX RANGE SCAN     NXIF312ACCOUNT_CROSS_FUNCTION     3           2                23     23
INDEX UNIQUE SCAN     PK_PRODUCT_PRODUCTKEY     867      2 K                         
This executes in 6 seconds
Any thoughts on why it takes 90 times longer to perform the Group By sort?

Answer 1

The plan didn't paste:
no group by:
Operation     Object Name     Rows     Bytes     Cost     Object Node     In/Out     PStart     PStop
SELECT STATEMENT Optimizer Mode=CHOOSE          3           6                     
NESTED LOOPS          3      60      6                     
TABLE ACCESS BY LOCAL INDEX ROWID     ACCOUNT_CROSS_FUNCTIONAL     3      33      3                23     23
INDEX RANGE SCAN     NXIF312ACCOUNT_CROSS_FUNCTION     3           2                23     23
TABLE ACCESS BY INDEX ROWID     PRODUCT     867      7 K     1                     
INDEX UNIQUE SCAN     PK_PRODUCT_PRODUCTKEY     867                               
group by:
Operation     Object Name     Rows     Bytes     Cost     Object Node     In/Out     PStart     PStop
SELECT STATEMENT Optimizer Mode=CHOOSE          3           10                     
SORT GROUP BY          3      60      10                     
NESTED LOOPS          3      60      6                     
TABLE ACCESS BY LOCAL INDEX ROWID     ACCOUNT_CROSS_FUNCTIONAL     3      33      3                23     23
INDEX RANGE SCAN     NXIF312ACCOUNT_CROSS_FUNCTION     3           2                23     23
TABLE ACCESS BY INDEX ROWID     PRODUCT     867      7 K     1                     
INDEX UNIQUE SCAN     PK_PRODUCT_PRODUCTKEY     867