Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
360 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 83 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. #26022064 | C2 | semidirect |
| 3. #26018229 | C2 | semidirect |
| 4. #26018226 | C2 | semidirect |
| 5. C89×#1455 | C2 | semidirect |
| 14. #19151419 | C22 | semidirect |
| 20. #322×C89 | C22 | semidirect |
| 21. C82×C89 | C22 | semidirect |
| 57. Dic356 | M16 | semidirect |
| 61. D712 | M16 | semidirect |
| 127. #1455 | D89 | semidirect |
| 130. C89 | #11669 | semidirect |
| 145. #322 | C2×D89 | semidirect |
| 146. C82 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029163 | 2 |
| #26022064 | 2 |
| #26018229 | 2 |
| #26018226 | 2 |
| C89×#1455 | 2 |
| #11669 | 89 |