Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
376 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 55 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. #26022466 | C2 | semidirect |
| 3. #26018242 | C2 | semidirect |
| 4. #26018188 | C2 | semidirect |
| 5. C89×#2091 | C2 | semidirect |
| 13. #19151380 | C22 | semidirect |
| 15. #430×C89 | C22 | semidirect |
| 18. #338×C89 | C22 | semidirect |
| 129. #2091 | D89 | semidirect |
| 132. C89 | #12298 | semidirect |
| 139. #430 | C2×D89 | semidirect |
| 145. #338 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031052 | 2 |
| #26022466 | 2 |
| #26018242 | 2 |
| #26018188 | 2 |
| C89×#2091 | 2 |
| #12298 | 89 |