Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
462 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 97 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. #22559897 | C2 | semidirect |
| 3. #22558970 | C2 | semidirect |
| 4. #22558819 | C2 | semidirect |
| 5. #22558718 | C2 | semidirect |
| 6. #22558717 | C2 | semidirect |
| 7. C67×#1530 | C2 | semidirect |
| 9. #16863799 | C4 | semidirect |
| 10. #16863772 | C4 | semidirect |
| 11. #16863744 | C4 | semidirect |
| 12. #16863742 | C4 | semidirect |
| 191. #1530 | D67 | semidirect |
| 194. C67 | #9762 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570784 | 2 |
| #22559897 | 2 |
| #22558970 | 2 |
| #22558819 | 2 |
| #22558718 | 2 |
| #22558717 | 2 |
| C67×#1530 | 2 |
| #9762 | 67 |