Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
580 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 580 conjugacy classes of subgroups — too many to draw. Only its 107 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. #22558230 | C2 | semidirect |
| 11. C23×Q8×C67 | C4 | semidirect |
| 14. #395×C67 | C4 | semidirect |
| 19. #380×C67 | C4 | semidirect |
| 178. C67 | #11898 | semidirect |
| 179. C23×Q8 | Dic67 | semidirect |
| 184. #395 | Dic67 | semidirect |
| 190. #380 | Dic67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22560197 | 2 |
| #22558530 | 2 |
| #22558230 | 2 |
| C67×#2409 | 2 |
| #11898 | 67 |