Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
650 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 650 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 2. #26022614 | C2 | semidirect |
| 3. #26021172 | C2 | semidirect |
| 4. #26018694 | C2 | semidirect |
| 5. #26018145 | C2 | semidirect |
| 6. #26018107 | C2 | semidirect |
| 7. C89×#1505 | C2 | semidirect |
| 11. #19151885 | C4 | semidirect |
| 12. #19151790 | C4 | semidirect |
| 46. C4⋊#10623494 | C2×C4 | semidirect |
| 57. C4⋊Q8×C89 | C2×C4 | semidirect |
| 58. #127×C89 | C2×C4 | semidirect |
| 158. D356 | #104 | semidirect |
| 200. #1505 | D89 | semidirect |
| 204. C89 | #9325 | semidirect |
| 232. C4⋊Q8 | C4×D89 | semidirect |
| 233. #127 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030339 | 2 |
| #26022614 | 2 |
| #26021172 | 2 |
| #26018694 | 2 |
| #26018145 | 2 |
| #26018107 | 2 |
| C89×#1505 | 2 |
| #9325 | 89 |