Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
248 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 65 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. #26022154 | C2 | semidirect |
| 3. #26019613 | C2 | semidirect |
| 4. #26019609 | C2 | semidirect |
| 5. #26018323 | C2 | semidirect |
| 6. #26018299 | C2 | semidirect |
| 7. C89×#1361 | C2 | semidirect |
| 60. #13083549 | SD16 | semidirect |
| 90. Dic178 | D16 | semidirect |
| 123. #1361 | D89 | semidirect |
| 124. C89 | #12439 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022501 | 2 |
| #26022154 | 2 |
| #26019613 | 2 |
| #26019609 | 2 |
| #26018323 | 2 |
| #26018299 | 2 |
| C89×#1361 | 2 |
| #12439 | 89 |