Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
442 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 85 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. #22569279 | C2 | semidirect |
| 3. #22558757 | C2 | semidirect |
| 4. #22558756 | C2 | semidirect |
| 5. #22558080 | C2 | semidirect |
| 6. #22558075 | C2 | semidirect |
| 7. C67×#1536 | C2 | semidirect |
| 9. #16863792 | C4 | semidirect |
| 10. #16863772 | C4 | semidirect |
| 11. #16863744 | C4 | semidirect |
| 12. #16863742 | C4 | semidirect |
| 170. #1536 | D67 | semidirect |
| 175. C67 | #9417 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570943 | 2 |
| #22569279 | 2 |
| #22558757 | 2 |
| #22558756 | 2 |
| #22558080 | 2 |
| #22558075 | 2 |
| C67×#1536 | 2 |
| #9417 | 67 |