Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
434 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 434 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 |
|---|---|---|
| 3. #22560257 | C2 | semidirect |
| 4. #22560253 | C2 | semidirect |
| 5. #22558339 | C2 | semidirect |
| 6. #22558337 | C2 | semidirect |
| 9. C23×C67⋊C8 | C4 | semidirect |
| 16. #16863423 | C4 | semidirect |
| 20. #16863360 | C4 | semidirect |
| 21. #16863352 | C4 | semidirect |
| 215. C67 | #12805 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22568904 | 2 |
| #22561850 | 2 |
| #22560257 | 2 |
| #22560253 | 2 |
| #22558339 | 2 |
| #22558337 | 2 |
| C67×#2120 | 2 |
| #12805 | 67 |