Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
736 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 736 conjugacy classes of subgroups — too many to draw. Only its 163 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. #22570950 | C2 | semidirect |
| 4. #22559872 | C2 | semidirect |
| 5. #22559867 | C2 | semidirect |
| 6. #22559866 | C2 | semidirect |
| 7. #22559822 | C2 | semidirect |
| 8. #22558512 | C2 | semidirect |
| 9. C67×#3185 | C2 | semidirect |
| 12. #16863792 | C22 | semidirect |
| 13. #16863775 | C22 | semidirect |
| 16. #16863748 | C22 | semidirect |
| 17. #16863746 | C22 | semidirect |
| 29. #16863118 | C22 | semidirect |
| 30. #16863117 | C22 | semidirect |
| 31. C8×C67⋊C8 | C22 | semidirect |
| 33. #498×C67 | C22 | semidirect |
| 34. #494×C67 | C22 | semidirect |
| 35. #487×C67 | C22 | semidirect |
| 161. #3185 | D67 | semidirect |
| 169. C67 | #19753 | semidirect |
| 174. #498 | C2×D67 | semidirect |
| 176. #494 | C2×D67 | semidirect |
| 181. #487 | C2×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570950 | 2 |
| #22570585 | 2 |
| #22570584 | 2 |
| #22559872 | 2 |
| #22559867 | 2 |
| #22559866 | 2 |
| #22559822 | 2 |
| #22558512 | 2 |
| C67×#3185 | 2 |
| #19753 | 67 |