Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
306 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 1. #26022525 | C2 | semidirect |
| 3. #26022477 | C2 | semidirect |
| 4. #26022475 | C2 | semidirect |
| 5. #26019844 | C2 | semidirect |
| 6. C8×#13083549 | C2 | semidirect |
| 7. C89×#1706 | C2 | semidirect |
| 55. #13083549 | SD16 | semidirect |
| 88. C8×C89 | D16 | semidirect |
| 115. #1706 | D89 | semidirect |
| 117. C89 | #12503 | semidirect |
| 198. C8 | #15667953 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022525 | 2 |
| #26022501 | 2 |
| #26022477 | 2 |
| #26022475 | 2 |
| #26019844 | 2 |
| C8×#13083549 | 2 |
| C89×#1706 | 2 |
| #12503 | 89 |