Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
396 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22561830 | C2 | semidirect |
| 2. #22560255 | C2 | semidirect |
| 3. #22558194 | C2 | semidirect |
| 9. #16863178 | C22 | semidirect |
| 10. #16863153 | C22 | semidirect |
| 11. C22×D8×C67 | C4 | semidirect |
| 14. #469×C67 | C4 | semidirect |
| 18. #427×C67 | C4 | semidirect |
| 155. C67 | #11868 | semidirect |
| 156. C22×D8 | Dic67 | semidirect |
| 160. #469 | Dic67 | semidirect |
| 165. #427 | Dic67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22561830 | 2 |
| #22560255 | 2 |
| #22558194 | 2 |
| C67×#3058 | 2 |
| #11868 | 67 |