Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
234 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 234 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 |
|---|---|---|
| 1. #26022501 | C2 | semidirect |
| 2. #26022329 | C2 | semidirect |
| 3. #26022325 | C2 | semidirect |
| 4. #26022088 | C2 | semidirect |
| 5. #26018327 | C2 | semidirect |
| 6. #26018288 | C2 | semidirect |
| 7. C89×#1357 | C2 | semidirect |
| 117. #1357 | D89 | semidirect |
| 118. C89 | #12436 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022501 | 2 |
| #26022329 | 2 |
| #26022325 | 2 |
| #26022088 | 2 |
| #26018327 | 2 |
| #26018288 | 2 |
| C89×#1357 | 2 |
| #12436 | 89 |