Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1172 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 1172 conjugacy classes of subgroups — too many to draw. Only its 167 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. C2×#19152224 | C2 | semidirect |
| 2. #26031058 | C2 | semidirect |
| 3. #26019276 | C2 | semidirect |
| 4. #26019174 | C2 | semidirect |
| 5. #26018771 | C2 | semidirect |
| 6. #26018579 | C2 | semidirect |
| 16. #19151933 | C22 | semidirect |
| 19. #19151749 | C22 | semidirect |
| 22. #19151334 | C22 | semidirect |
| 33. C22×Dic178 | D4 | semidirect |
| 42. #15667991 | D4 | semidirect |
| 49. C2×C4⋊Dic89 | D4 | semidirect |
| 242. C89 | #18318 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152224 | 2 |
| #26031058 | 2 |
| #26019276 | 2 |
| #26019174 | 2 |
| #26018771 | 2 |
| #26018579 | 2 |
| C89×#2539 | 2 |
| #18318 | 89 |