SELECT object_type, COUNT(*) as obj_cnt
FROM dba_objects
WHERE owner IN (SELECT username FROM dba_users WHERE oracle_maintained = 'Y')
GROUP BY ROLLUP(object_type)
ORDER BY object_type NULLS LAST;

OBJECT_TYPE                OBJ_CNT
----------------------- ----------
CLUSTER                         10
CONSUMER GROUP                  18
CONTAINER                        2
CONTEXT                         18
DATABASE LINK                    1
DESTINATION                      2
DIRECTORY                       15
EDITION                          1
EVALUATION CONTEXT              14
FUNCTION                       381
INDEX                         2923
INDEX PARTITION                631
INDEXTYPE                       11
JAVA CLASS                   37367
JAVA DATA                     1221
JAVA RESOURCE                 1693
JAVA SOURCE                      2
JOB                             24
JOB CLASS                       16
LIBRARY                        250
LOB                            701
LOB PARTITION                   89
OPERATOR                        60
PACKAGE                       1083
PACKAGE BODY                  1032
PROCEDURE                      232
PROGRAM                         10
QUEUE                           27
RESOURCE PLAN                   11
RULE                             1
RULE SET                        21
SCHEDULE                         4
SCHEDULER GROUP                  4
SEQUENCE                       310
SYNONYM                         40
TABLE                         2241
TABLE PARTITION                714
TABLE SUBPARTITION              32
TRIGGER                        137
TYPE                          2868
TYPE BODY                      286
UNDEFINED                       15
UNIFIED AUDIT POLICY             9
VIEW                          7329
WINDOW                           9
XML SCHEMA                      43
                             61908

47 rows selected.