Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
712 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 712 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. C2×#16863836 | C2 | semidirect |
| 2. C22×#14523988 | C2 | semidirect |
| 4. #22569076 | C2 | semidirect |
| 5. #22562274 | C2 | semidirect |
| 6. #22562248 | C2 | semidirect |
| 7. #22561967 | C2 | semidirect |
| 8. #22561924 | C2 | semidirect |
| 9. C67×#2138 | C2 | semidirect |
| 16. C2×#14523989 | C22 | semidirect |
| 19. C2×#14523987 | C22 | semidirect |
| 25. #16863490 | C22 | semidirect |
| 28. Dic67⋊C16 | C22 | semidirect |
| 33. #358×C67 | C22 | semidirect |
| 34. #357×C67 | C22 | semidirect |
| 40. C2×Dic268 | D4 | semidirect |
| 185. #2138 | D67 | semidirect |
| 186. C67 | #33587 | semidirect |
| 209. #358 | C2×D67 | semidirect |
| 211. #357 | C2×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863836 | 2 |
| C22×#14523988 | 2 |
| #22570696 | 2 |
| #22569076 | 2 |
| #22562274 | 2 |
| #22562248 | 2 |
| #22561967 | 2 |
| #22561924 | 2 |
| C67×#2138 | 2 |
| #33587 | 67 |