Oracle 11g Count query slowness - oracle

Question

I have written one query which provides me a count of item type using group by.
The select query if I fire without group up and count provides results in less than a second on sql developer.
However count query runs for ever that I have to kill the process.
Below is the query ..
WITH permList
AS (SELECT user_perm_level,
item_category,
active
FROM usr_perm_levels
WHERE usr_pk = '7'
UNION ALL
SELECT home_key,
'ALL',
0
FROM user_home_list
WHERE usr_pk = 7
UNION ALL
SELECT home_key,
'UYT',
0
FROM user_home_list
WHERE usr_pk = 7
UNION ALL
SELECT home_key,
'ABR',
0
FROM user_home_list
WHERE usr_pk = 7),
list1
AS (SELECT a.parent_home_key,
b.item_category
FROM user_hier a
INNER JOIN indhome b
ON a.child_home_key = b.user_perm_level),
list2
AS ((SELECT oh.child_home_key,
u.item_category
FROM indhome U
INNER JOIN user_hier oh
ON u.user_perm_level = oh.parent_home_key
AND u.active = 1)
UNION ALL
SELECT user_perm_level,
item_category
FROM indhome)
SELECT type,
Count(*)
FROM inventory
WHERE is_available = 0
AND active = 1
AND EXISTS (SELECT 0
FROM inventory_auth c
WHERE EXISTS (SELECT 0
FROM orglist1
WHERE c.user_perm_level = orglist1.parent_home_key
AND c.item_category =
orglist1.item_category
AND c.active = 1)
OR EXISTS (SELECT 0
FROM orglist2
WHERE c.user_perm_level = orglist2.child_home_key
AND c.item_category =
orglist2.item_category)
AND inventory.item_key = c.item_key
AND inventory.item_category = c.item_category)
GROUP BY type;
In explain plan I see that Cost of group by clause is 145297221173.
Now here inventory table has 10 million records and the exists block which works around inventory table also runs into 15 million records.
Where as views permList, list1 and list2 have records only in 100s.
I have tried various combination but none of them seems to bring better performance. Such as I have tried inner join between inventory and inner query with exists clause but that doesn't help much.