Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
512 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 135 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. #22620590 | C2 | semidirect |
| 2. #22612150 | C2 | semidirect |
| 3. #22612107 | C2 | semidirect |
| 4. #22612012 | C2 | semidirect |
| 6. #22611822 | C2 | semidirect |
| 7. #22611747 | C2 | semidirect |
| 11. #17988989 | C22 | semidirect |
| 12. #17988967 | C22 | semidirect |
| 16. #17988695 | C22 | semidirect |
| 18. #17988411 | C22 | semidirect |
| 19. #17988408 | C22 | semidirect |
| 20. #17988402 | C22 | semidirect |
| 23. #17988365 | C22 | semidirect |
| 169. C73 | #33693 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620590 | 2 |
| #22612150 | 2 |
| #22612107 | 2 |
| #22612012 | 2 |
| #22611882 | 2 |
| #22611822 | 2 |
| #22611747 | 2 |
| C73×#2955 | 2 |
| #33693 | 73 |