Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
1132 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 1132 conjugacy classes of subgroups — too many to draw. Only its 179 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22571124 | C2 | semidirect |
| 2. #22570662 | C2 | semidirect |
| 3. #22559292 | C2 | semidirect |
| 4. #22559263 | C2 | semidirect |
| 5. #22558871 | C2 | semidirect |
| 6. #22558626 | C2 | semidirect |
| 7. C67×#3549 | C2 | semidirect |
| 9. C2×#14524040 | C22 | semidirect |
| 13. #16863770 | C22 | semidirect |
| 15. #16863591 | C22 | semidirect |
| 17. #16863449 | C22 | semidirect |
| 18. C4×#11761612 | C22 | semidirect |
| 19. #16863145 | C22 | semidirect |
| 20. #16863140 | C22 | semidirect |
| 21. D4⋊(C67⋊C8) | C22 | semidirect |
| 24. #555×C67 | C22 | semidirect |
| 26. D42×C67 | C22 | semidirect |
| 180. #3549 | D67 | semidirect |
| 187. C67 | #18714 | semidirect |
| 191. #555 | C2×D67 | semidirect |
| 193. D42 | C2×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571124 | 2 |
| #22570662 | 2 |
| #22559292 | 2 |
| #22559263 | 2 |
| #22558871 | 2 |
| #22558626 | 2 |
| C67×#3549 | 2 |
| #18714 | 67 |