Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
388 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 77 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. #26020371 | C2 | semidirect |
| 3. #26018945 | C2 | semidirect |
| 4. #26018761 | C2 | semidirect |
| 5. #26018760 | C2 | semidirect |
| 6. #26018121 | C2 | semidirect |
| 7. C89×#1551 | C2 | semidirect |
| 168. #1551 | D89 | semidirect |
| 172. C89 | #10513 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031559 | 2 |
| #26020371 | 2 |
| #26018945 | 2 |
| #26018761 | 2 |
| #26018760 | 2 |
| #26018121 | 2 |
| C89×#1551 | 2 |
| #10513 | 89 |