Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
352 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 81 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. #22562009 | C2 | semidirect |
| 3. #22560101 | C2 | semidirect |
| 4. #22558222 | C2 | semidirect |
| 5. #22558220 | C2 | semidirect |
| 9. #16863797 | C4 | semidirect |
| 10. #16863779 | C4 | semidirect |
| 14. #16863490 | C4 | semidirect |
| 16. D8×Dic67 | C4 | semidirect |
| 169. C67 | #11746 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570774 | 2 |
| #22562009 | 2 |
| #22560101 | 2 |
| #22558222 | 2 |
| #22558220 | 2 |
| #22558218 | 2 |
| C67×#1347 | 2 |
| #11746 | 67 |