Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
442 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 59 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. #26031117 | C2 | semidirect |
| 2. #26022164 | C2 | semidirect |
| 3. #26018266 | C2 | semidirect |
| 4. #26018178 | C2 | semidirect |
| 5. C89×#2018 | C2 | semidirect |
| 13. C22⋊#13083549 | C22 | semidirect |
| 15. C22×D8×C89 | C22 | semidirect |
| 18. #341×C89 | C22 | semidirect |
| 147. #2018 | D89 | semidirect |
| 150. C89 | #12108 | semidirect |
| 152. C22×D8 | C2×D89 | semidirect |
| 163. #341 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031117 | 2 |
| #26022164 | 2 |
| #26018266 | 2 |
| #26018178 | 2 |
| C89×#2018 | 2 |
| #12108 | 89 |