Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
716 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 716 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 |
|---|---|---|
| 2. C22×#14523988 | C2 | semidirect |
| 3. #22570704 | C2 | semidirect |
| 4. #22569060 | C2 | semidirect |
| 5. #22562263 | C2 | semidirect |
| 6. #22562253 | C2 | semidirect |
| 7. #22561967 | C2 | semidirect |
| 8. #22561928 | C2 | semidirect |
| 9. C67×#2138 | C2 | semidirect |
| 22. #16863779 | C22 | semidirect |
| 23. #16863774 | C22 | semidirect |
| 28. Dic67⋊C16 | C22 | semidirect |
| 29. #16863199 | C22 | semidirect |
| 33. #358×C67 | C22 | semidirect |
| 34. #357×C67 | C22 | semidirect |
| 185. #2138 | D67 | semidirect |
| 186. C67 | #33586 | semidirect |
| 210. #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×#16863831 | 2 |
| C22×#14523988 | 2 |
| #22570704 | 2 |
| #22569060 | 2 |
| #22562263 | 2 |
| #22562253 | 2 |
| #22561967 | 2 |
| #22561928 | 2 |
| C67×#2138 | 2 |
| #33586 | 67 |