Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1034 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 1034 conjugacy classes of subgroups — too many to draw. Only its 115 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. #26022830 | C2 | semidirect |
| 2. #26020173 | C2 | semidirect |
| 3. #26018781 | C2 | semidirect |
| 4. #26018105 | C2 | semidirect |
| 14. C2×#127×C89 | C4 | semidirect |
| 19. #390×C89 | C4 | semidirect |
| 32. #15667919 | D4 | semidirect |
| 42. C22×D4×C89 | C2×C4 | semidirect |
| 50. C2×C4⋊C4×C89 | C2×C4 | semidirect |
| 55. C2×C42×C89 | C2×C4 | semidirect |
| 226. C89 | #9463 | semidirect |
| 228. C2×#127 | Dic89 | semidirect |
| 236. #390 | Dic89 | semidirect |
| 251. C22×D4 | C2×Dic89 | semidirect |
| 261. C2×C4⋊C4 | C2×Dic89 | semidirect |
| 271. C2×C42 | C2×Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022830 | 2 |
| #26020173 | 2 |
| #26018781 | 2 |
| #26018105 | 2 |
| C89×#2433 | 2 |
| #9463 | 89 |