Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
394 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 89 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. #22562005 | C2 | semidirect |
| 3. #22560101 | C2 | semidirect |
| 4. #22558219 | C2 | semidirect |
| 5. #22558218 | C2 | semidirect |
| 6. #22558217 | C2 | semidirect |
| 7. C67×#1347 | C2 | semidirect |
| 9. #16863800 | C4 | semidirect |
| 10. #16863771 | C4 | semidirect |
| 14. D8×Dic67 | C4 | semidirect |
| 15. #16863478 | C4 | semidirect |
| 179. #1347 | D67 | semidirect |
| 180. C67 | #11742 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570783 | 2 |
| #22562005 | 2 |
| #22560101 | 2 |
| #22558219 | 2 |
| #22558218 | 2 |
| #22558217 | 2 |
| C67×#1347 | 2 |
| #11742 | 67 |