Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
498 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 79 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. #22611596 | C2 | semidirect |
| 2. #22608523 | C2 | semidirect |
| 3. #22608082 | C2 | semidirect |
| 7. #17988382 | C22 | semidirect |
| 10. #17988327 | C22 | semidirect |
| 11. #585×C73 | C4 | semidirect |
| 14. #456×C73 | C4 | semidirect |
| 19. #413×C73 | C4 | semidirect |
| 179. C73 | #13568 | semidirect |
| 180. #585 | Dic73 | semidirect |
| 183. #456 | Dic73 | semidirect |
| 188. #413 | Dic73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22611596 | 2 |
| #22608523 | 2 |
| #22608082 | 2 |
| C73×#3018 | 2 |
| #13568 | 73 |