Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
992 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 992 conjugacy classes of subgroups — too many to draw. Only its 171 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. #22571220 | C2 | semidirect |
| 2. #22570554 | C2 | semidirect |
| 3. #22559515 | C2 | semidirect |
| 4. #22558844 | C2 | semidirect |
| 5. #22558820 | C2 | semidirect |
| 7. #16863953 | C22 | semidirect |
| 8. #16863791 | C22 | semidirect |
| 11. #16863755 | C22 | semidirect |
| 12. #16863755 | C22 | semidirect |
| 16. #16863453 | C22 | semidirect |
| 18. C2×#14523954 | C22 | semidirect |
| 19. #16863136 | C22 | semidirect |
| 20. #16863136 | C22 | semidirect |
| 177. C67 | #19056 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571220 | 2 |
| #22570554 | 2 |
| #22559515 | 2 |
| #22558844 | 2 |
| #22558820 | 2 |
| C67×#3549 | 2 |
| #19056 | 67 |