Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
808 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 808 conjugacy classes of subgroups — too many to draw. Only its 83 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. #26031059 | C2 | semidirect |
| 2. #26029512 | C2 | semidirect |
| 4. #26021237 | C2 | semidirect |
| 5. #26018767 | C2 | semidirect |
| 6. #26018157 | C2 | semidirect |
| 7. C89×#1789 | C2 | semidirect |
| 33. C22×Dic178 | D4 | semidirect |
| 53. C2×C4⋊Dic89 | D4 | semidirect |
| 66. C22⋊#10623494 | D4 | semidirect |
| 79. C2×M16×C89 | D4 | semidirect |
| 274. #1789 | D89 | semidirect |
| 277. C89 | #9934 | semidirect |
| 322. C2×M16 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031059 | 2 |
| #26029512 | 2 |
| #26025976 | 2 |
| #26021237 | 2 |
| #26018767 | 2 |
| #26018157 | 2 |
| C89×#1789 | 2 |
| #9934 | 89 |