Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
960 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 960 conjugacy classes of subgroups — too many to draw. Only its 155 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 |
|---|---|---|
| 1. C2×#16864144 | C2 | semidirect |
| 2. #22571192 | C2 | semidirect |
| 3. #22559530 | C2 | semidirect |
| 4. #22559501 | C2 | semidirect |
| 5. #22558836 | C2 | semidirect |
| 6. #22558806 | C2 | semidirect |
| 7. C67×#3142 | C2 | semidirect |
| 15. #16863783 | C22 | semidirect |
| 16. #16863758 | C22 | semidirect |
| 21. #16863138 | C22 | semidirect |
| 22. #16863135 | C22 | semidirect |
| 25. #491×C67 | C22 | semidirect |
| 26. #490×C67 | C22 | semidirect |
| 167. #3142 | D67 | semidirect |
| 172. C67 | #19001 | semidirect |
| 183. #491 | C2×D67 | semidirect |
| 184. #490 | C2×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16864144 | 2 |
| #22571192 | 2 |
| #22559530 | 2 |
| #22559501 | 2 |
| #22558836 | 2 |
| #22558806 | 2 |
| C67×#3142 | 2 |
| #19001 | 67 |