Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
422 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 103 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. #22558721 | C2 | semidirect |
| 4. #22558682 | C2 | semidirect |
| 5. #22558071 | C2 | semidirect |
| 6. #22558037 | C2 | semidirect |
| 22. #500×C67 | C4 | semidirect |
| 23. #498×C67 | C4 | semidirect |
| 24. #486×C67 | C4 | semidirect |
| 25. #486×C67 | C4 | semidirect |
| 176. C67 | #9279 | semidirect |
| 179. #500 | Dic67 | semidirect |
| 180. #498 | Dic67 | semidirect |
| 181. #486 | Dic67 | semidirect |
| 182. #486 | Dic67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569285 | 2 |
| #22558721 | 2 |
| #22558717 | 2 |
| #22558682 | 2 |
| #22558071 | 2 |
| #22558037 | 2 |
| C67×#3228 | 2 |
| #9279 | 67 |