Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1056 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 1056 conjugacy classes of subgroups — too many to draw. Only its 179 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. #22621056 | C2 | semidirect |
| 2. #22620391 | C2 | semidirect |
| 3. #22609076 | C2 | semidirect |
| 4. #22609047 | C2 | semidirect |
| 5. #22608593 | C2 | semidirect |
| 6. #22608348 | C2 | semidirect |
| 9. C2×#14556591 | C22 | semidirect |
| 12. #17988966 | C22 | semidirect |
| 16. #17988877 | C22 | semidirect |
| 17. #17988640 | C22 | semidirect |
| 18. C4×#11924012 | C22 | semidirect |
| 19. #17988336 | C22 | semidirect |
| 21. D4⋊#10596831 | C22 | semidirect |
| 179. C73 | #18715 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22621056 | 2 |
| #22620391 | 2 |
| #22609076 | 2 |
| #22609047 | 2 |
| #22608593 | 2 |
| #22608348 | 2 |
| C73×#3549 | 2 |
| #18715 | 73 |