Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
748 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 748 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×#16863831 | C2 | semidirect |
| 2. C22×D1072 | C2 | semidirect |
| 3. #22570696 | C2 | semidirect |
| 4. #22569060 | C2 | semidirect |
| 5. #22562267 | C2 | semidirect |
| 6. #22562243 | C2 | semidirect |
| 7. #22561967 | C2 | semidirect |
| 8. #22561924 | C2 | semidirect |
| 9. C67×#2138 | C2 | semidirect |
| 16. C2×#14523986 | C22 | semidirect |
| 19. C2×#14523984 | C22 | semidirect |
| 22. #16863781 | C22 | semidirect |
| 23. #16863771 | C22 | semidirect |
| 25. #16863478 | C22 | semidirect |
| 28. Dic67⋊C16 | C22 | semidirect |
| 29. #16863196 | C22 | semidirect |
| 33. #358×C67 | C22 | semidirect |
| 34. #357×C67 | C22 | semidirect |
| 44. C2×D536 | D4 | semidirect |
| 190. #2138 | D67 | semidirect |
| 191. C67 | #33585 | semidirect |
| 214. #358 | C2×D67 | semidirect |
| 216. #357 | C2×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863831 | 2 |
| C22×D1072 | 2 |
| #22570696 | 2 |
| #22569060 | 2 |
| #22562267 | 2 |
| #22562243 | 2 |
| #22561967 | 2 |
| #22561924 | 2 |
| C67×#2138 | 2 |
| #33585 | 67 |