Minimum coverings by 6-cycles

There are 3 nonisomorphic minimum coverings by 6-cycles for n = 6:
1.  (0,1,2,3,4,5) (0,1,3,2,5,4) (0,2,4,1,5,3)
2.  (0,1,2,3,4,5) (0,1,3,5,2,4) (0,2,4,1,5,3)
3.  (0,1,2,3,4,5) (0,1,3,5,2,4) (0,2,5,1,4,3)

There are 10 nonisomorphic minimum coverings by 6-cycles for n = 7:
1.  (0,1,2,3,4,5) (0,1,2,4,6,3) (0,2,5,3,1,6) (0,2,6,5,1,4)
2.  (0,1,2,3,4,5) (0,1,2,5,3,6) (0,2,4,6,1,3) (0,2,6,5,1,4)
3.  (0,1,2,3,4,5) (0,1,3,5,2,6) (0,2,1,5,6,4) (0,2,4,1,6,3)
4.  (0,1,2,3,4,5) (0,1,3,5,2,6) (0,2,4,1,6,3) (0,3,1,5,6,4)
5.  (0,1,2,3,4,5) (0,1,3,5,2,6) (0,2,4,6,1,3) (0,3,6,5,1,4)
6.  (0,1,2,3,4,5) (0,1,3,5,2,6) (0,2,4,6,1,5) (0,3,6,5,1,4)
7.  (0,1,2,3,4,5) (0,1,3,5,6,2) (0,2,1,4,6,3) (0,4,2,5,1,6)
8.  (0,1,2,3,4,5) (0,1,3,5,6,4) (0,2,4,1,6,3) (0,3,1,5,2,6)
9.  (0,1,2,3,4,5) (0,1,3,5,6,4) (0,2,5,1,6,3) (0,3,1,4,2,6)
10.  (0,1,2,3,4,5) (0,1,3,6,4,2) (0,2,1,6,5,3) (0,4,1,5,2,6)