Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
464 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 2. #22569269 | C2 | semidirect |
| 3. #22558763 | C2 | semidirect |
| 4. #22558569 | C2 | semidirect |
| 5. #22558117 | C2 | semidirect |
| 6. #22558085 | C2 | semidirect |
| 7. C67×#1510 | C2 | semidirect |
| 9. #16863726 | C4 | semidirect |
| 11. #16863709 | C4 | semidirect |
| 14. #16863547 | C4 | semidirect |
| 16. #16863530 | C4 | semidirect |
| 229. #1510 | D67 | semidirect |
| 233. C67 | #9332 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571023 | 2 |
| #22569269 | 2 |
| #22558763 | 2 |
| #22558569 | 2 |
| #22558117 | 2 |
| #22558085 | 2 |
| C67×#1510 | 2 |
| #9332 | 67 |