Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
474 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 91 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. #22569224 | C2 | semidirect |
| 3. #22560020 | C2 | semidirect |
| 4. #22558800 | C2 | semidirect |
| 5. #22558716 | C2 | semidirect |
| 6. #22558080 | C2 | semidirect |
| 7. C67×#1300 | C2 | semidirect |
| 11. #16863682 | C4 | semidirect |
| 12. #16863677 | C4 | semidirect |
| 13. #16863597 | C4 | semidirect |
| 14. #16863592 | C4 | semidirect |
| 208. #1300 | D67 | semidirect |
| 210. C67 | #9161 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570361 | 2 |
| #22569224 | 2 |
| #22560020 | 2 |
| #22558800 | 2 |
| #22558716 | 2 |
| #22558080 | 2 |
| C67×#1300 | 2 |
| #9161 | 67 |