Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
810 conjugacy classes of subgroups; only the 176 normal subgroups are shown.
This group has 810 conjugacy classes of subgroups — too many to draw. Only its 176 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. #22626660 | C2 | semidirect |
| 2. #22626069 | C2 | semidirect |
| 3. #22625922 | C2 | semidirect |
| 4. #22625856 | C2 | semidirect |
| 5. #22625649 | C2 | semidirect |
| 18. #17988970 | C4 | semidirect |
| 19. #17988967 | C4 | semidirect |
| 20. #17988959 | C4 | semidirect |
| 22. #493×C73 | C4 | semidirect |
| 120. C73 | #22282 | semidirect |
| 126. #493 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626660 | 2 |
| #22626069 | 2 |
| #22625922 | 2 |
| #22625856 | 2 |
| #22625649 | 2 |
| #22620358 | 2 |
| #22282 | 73 |