Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
372 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 61 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. #26022330 | C2 | semidirect |
| 3. #26019859 | C2 | semidirect |
| 4. #26018288 | C2 | semidirect |
| 5. #26018225 | C2 | semidirect |
| 6. #26018224 | C2 | semidirect |
| 7. C89×#2214 | C2 | semidirect |
| 17. #19151419 | C22 | semidirect |
| 19. C8×#10623494 | C22 | semidirect |
| 21. #494×C89 | C22 | semidirect |
| 23. #364×C89 | C22 | semidirect |
| 147. #2214 | D89 | semidirect |
| 152. C89 | #12312 | semidirect |
| 157. #494 | C2×D89 | semidirect |
| 166. #364 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26032052 | 2 |
| #26022330 | 2 |
| #26019859 | 2 |
| #26018288 | 2 |
| #26018225 | 2 |
| #26018224 | 2 |
| C89×#2214 | 2 |
| #12312 | 89 |