Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
576 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 103 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. #26023364 | C2 | semidirect |
| 2. #26018876 | C2 | semidirect |
| 3. #26018760 | C2 | semidirect |
| 4. #26018146 | C2 | semidirect |
| 19. #497×C89 | C4 | semidirect |
| 20. #496×C89 | C4 | semidirect |
| 48. C4⋊Q8×C89 | C2×C4 | semidirect |
| 49. #127×C89 | C2×C4 | semidirect |
| 58. #97×C89 | C2×C4 | semidirect |
| 176. C89 | #9441 | semidirect |
| 181. #497 | Dic89 | semidirect |
| 182. #496 | Dic89 | semidirect |
| 207. C4⋊Q8 | C2×Dic89 | semidirect |
| 208. #127 | C2×Dic89 | semidirect |
| 225. #97 | C2×Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023364 | 2 |
| #26018876 | 2 |
| #26018760 | 2 |
| #26018146 | 2 |
| C89×#3153 | 2 |
| #9441 | 89 |