Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
248 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 63 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. #26019845 | C2 | semidirect |
| 3. #26019137 | C2 | semidirect |
| 4. #26018321 | C2 | semidirect |
| 5. #26018310 | C2 | semidirect |
| 6. #26018299 | C2 | semidirect |
| 7. C89×#2226 | C2 | semidirect |
| 115. #2226 | D89 | semidirect |
| 122. C89 | #12485 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022287 | 2 |
| #26019845 | 2 |
| #26019137 | 2 |
| #26018321 | 2 |
| #26018310 | 2 |
| #26018299 | 2 |
| C89×#2226 | 2 |
| #12485 | 89 |