Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
686 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 686 conjugacy classes of subgroups — too many to draw. Only its 93 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. #26018565 | C2 | semidirect |
| 3. #26018184 | C2 | semidirect |
| 4. #26018183 | C2 | semidirect |
| 5. C89×#1318 | C2 | semidirect |
| 15. #19151324 | C22 | semidirect |
| 18. #324×C89 | C22 | semidirect |
| 25. C2×D4×D89 | C8 | semidirect |
| 180. #1318 | D89 | semidirect |
| 181. C89 | #11433 | semidirect |
| 193. #324 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022831 | 2 |
| #26018565 | 2 |
| #26018184 | 2 |
| #26018183 | 2 |
| C89×#1318 | 2 |
| #11433 | 89 |