Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
460 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 3. #26020459 | C2 | semidirect |
| 4. #26020456 | C2 | semidirect |
| 6. #26018140 | C2 | semidirect |
| 7. C89×#1298 | C2 | semidirect |
| 138. C22×D89 | #108 | semidirect |
| 213. #1298 | D89 | semidirect |
| 214. C89 | #8859 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029279 | 2 |
| #26020547 | 2 |
| #26020459 | 2 |
| #26020456 | 2 |
| #26018568 | 2 |
| #26018140 | 2 |
| C89×#1298 | 2 |
| #8859 | 89 |