Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
318 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 71 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. #26022534 | C2 | semidirect |
| 3. #26022400 | C2 | semidirect |
| 4. #26019651 | C2 | semidirect |
| 5. #26018306 | C2 | semidirect |
| 6. #26018214 | C2 | semidirect |
| 7. C89×D4⋊C16 | C2 | semidirect |
| 138. D4⋊C16 | D89 | semidirect |
| 139. C89 | #12396 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26032600 | 2 |
| #26022534 | 2 |
| #26022400 | 2 |
| #26019651 | 2 |
| #26018306 | 2 |
| #26018214 | 2 |
| C89×D4⋊C16 | 2 |
| #12396 | 89 |