Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
488 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 93 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. #26029388 | C2 | semidirect |
| 3. #26021049 | C2 | semidirect |
| 4. #26018841 | C2 | semidirect |
| 5. #26018696 | C2 | semidirect |
| 6. #26018152 | C2 | semidirect |
| 7. C89×#1283 | C2 | semidirect |
| 234. #1283 | D89 | semidirect |
| 235. C89 | #9052 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030301 | 2 |
| #26029388 | 2 |
| #26021049 | 2 |
| #26018841 | 2 |
| #26018696 | 2 |
| #26018152 | 2 |
| C89×#1283 | 2 |
| #9052 | 89 |