Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
650 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 650 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. #26022613 | C2 | semidirect |
| 2. #26021172 | C2 | semidirect |
| 3. #26018760 | C2 | semidirect |
| 4. #26018695 | C2 | semidirect |
| 5. #26018144 | C2 | semidirect |
| 6. #26018109 | C2 | semidirect |
| 24. #476×C89 | C4 | semidirect |
| 25. #459×C89 | C4 | semidirect |
| 52. C4⋊Q8×C89 | C2×C4 | semidirect |
| 53. #127×C89 | C2×C4 | semidirect |
| 67. C4⋊C8×C89 | C2×C4 | semidirect |
| 135. D4×C89 | #104 | semidirect |
| 204. C89 | #9325 | semidirect |
| 209. #476 | Dic89 | semidirect |
| 210. #459 | Dic89 | semidirect |
| 232. C4⋊Q8 | C2×Dic89 | semidirect |
| 233. #127 | C2×Dic89 | semidirect |
| 254. C4⋊C8 | C2×Dic89 | semidirect |
| 332. D4 | #15667939 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022613 | 2 |
| #26021172 | 2 |
| #26018760 | 2 |
| #26018695 | 2 |
| #26018144 | 2 |
| #26018109 | 2 |
| C89×#3109 | 2 |
| #9325 | 89 |