Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
996 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 996 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. #22571596 | C2 | semidirect |
| 2. #22570531 | C2 | semidirect |
| 3. #22559437 | C2 | semidirect |
| 4. #22559388 | C2 | semidirect |
| 5. #22558944 | C2 | semidirect |
| 6. #22558660 | C2 | semidirect |
| 8. #16863953 | C22 | semidirect |
| 10. #16863746 | C22 | semidirect |
| 13. #16863676 | C22 | semidirect |
| 15. #16863601 | C22 | semidirect |
| 17. #16863420 | C22 | semidirect |
| 19. C2×C4×C67⋊C8 | C22 | semidirect |
| 20. #16863145 | C22 | semidirect |
| 22. D4⋊(C67⋊C8) | C22 | semidirect |
| 187. C67 | #18691 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571596 | 2 |
| #22570531 | 2 |
| #22559437 | 2 |
| #22559388 | 2 |
| #22558944 | 2 |
| #22558660 | 2 |
| C67×#3549 | 2 |
| #18691 | 67 |