Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
448 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 95 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. #22561903 | C2 | semidirect |
| 4. #22561864 | C2 | semidirect |
| 6. #22560009 | C2 | semidirect |
| 7. C67×#1813 | C2 | semidirect |
| 8. C22×#11761617 | C4 | semidirect |
| 15. #16863434 | C4 | semidirect |
| 16. #16863406 | C4 | semidirect |
| 17. #16863402 | C4 | semidirect |
| 216. #1813 | D67 | semidirect |
| 218. C67 | #13232 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569848 | 2 |
| #22561903 | 2 |
| #22561900 | 2 |
| #22561864 | 2 |
| #22561860 | 2 |
| #22560009 | 2 |
| C67×#1813 | 2 |
| #13232 | 67 |