Maximum packings with 6-cycles

There are 2 nonisomorphic maximum packings with 6-cycles when n = 7:
1.  (0,1,2,3,4,5) (0,2,4,1,3,6) (0,3,5,1,6,4)
2.  (0,1,2,3,4,5) (0,2,4,1,3,6) (0,3,5,2,6,4)

There are 22 nonisomorphic maximum packings with 6-cycles when n = 8:
1.  (0,1,2,3,4,5) (0,2,4,1,6,7) (0,3,1,7,5,6) (2,5,3,6,4,7)
2.  (0,1,2,3,4,5) (0,2,4,1,6,7) (0,3,1,7,5,6) (2,5,3,7,4,6)
3.  (0,1,2,3,4,5) (0,2,4,1,6,7) (0,3,5,7,2,6) (1,3,7,4,6,5)
4.  (0,1,2,3,4,5) (0,2,4,1,6,7) (0,3,5,7,4,6) (1,3,6,5,2,7)
5.  (0,1,2,3,4,5) (0,2,4,1,6,7) (0,3,7,1,5,6) (2,5,3,6,4,7)
6.  (0,1,2,3,4,5) (0,2,4,1,6,7) (0,3,7,2,5,6) (1,3,6,4,7,5)
7.  (0,1,2,3,4,5) (0,2,4,1,6,7) (0,3,7,2,5,6) (1,5,3,6,4,7)
8.  (0,1,2,3,4,5) (0,2,4,1,6,7) (0,3,7,5,2,6) (1,3,5,6,4,7)
9.  (0,1,2,3,4,5) (0,2,4,1,6,7) (0,3,7,5,6,4) (1,5,3,6,2,7)
10.  (0,1,2,3,4,5) (0,2,4,6,1,7) (0,3,5,6,7,4) (1,3,6,2,7,5)
11.  (0,1,2,3,4,5) (0,2,4,6,1,7) (0,4,7,3,5,6) (1,3,6,2,7,5)
12.  (0,1,2,3,4,5) (0,2,4,6,1,7) (0,4,7,5,3,6) (1,3,7,2,6,5)
13.  (0,1,2,3,4,5) (0,2,4,6,5,7) (0,3,1,4,7,6) (1,5,3,6,2,7)
14.  (0,1,2,3,4,5) (0,2,4,6,5,7) (0,3,1,4,7,6) (1,5,3,7,2,6)
15.  (0,1,2,3,4,5) (0,2,4,6,5,7) (0,3,1,6,7,4) (1,5,3,6,2,7)
16.  (0,1,2,3,4,5) (0,2,4,6,5,7) (0,3,7,4,1,6) (1,5,3,6,2,7)
17.  (0,1,2,3,4,5) (0,2,5,1,6,7) (0,3,7,1,4,6) (2,4,7,5,3,6)
18.  (0,1,2,3,4,5) (0,2,5,1,6,7) (0,4,7,1,3,6) (2,4,6,5,3,7)
19.  (0,1,2,3,4,5) (0,2,5,3,6,7) (0,4,7,3,1,6) (1,4,2,6,5,7)
20.  (0,1,2,3,4,5) (0,2,5,3,6,7) (0,4,7,3,1,6) (1,5,6,4,2,7)
21.  (0,1,2,3,4,5) (0,2,5,6,7,3) (0,4,6,3,1,7) (1,5,7,4,2,6)
22.  (0,1,2,3,4,5) (0,2,6,3,5,7) (0,4,7,3,1,6) (1,5,6,4,2,7)