Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1946 conjugacy classes of subgroups; only the 259 normal subgroups are shown.
This group has 1946 conjugacy classes of subgroups — too many to draw. Only its 259 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. #26028881 | C2 | semidirect |
| 3. #26021090 | C2 | semidirect |
| 4. #26020173 | C2 | semidirect |
| 5. #26020172 | C2 | semidirect |
| 6. C89×#1783 | C2 | semidirect |
| 16. #19151621 | C22 | semidirect |
| 17. C2×#15667929 | C22 | semidirect |
| 18. C2×#15667928 | C22 | semidirect |
| 20. M16×Dic89 | C22 | semidirect |
| 22. C2×#100×C89 | C22 | semidirect |
| 137. C2×Dic89 | #100 | semidirect |
| 176. #1783 | D89 | semidirect |
| 177. C89 | #21797 | semidirect |
| 191. C2×#100 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668008 | 2 |
| #26028881 | 2 |
| #26021090 | 2 |
| #26020173 | 2 |
| #26020172 | 2 |
| C89×#1783 | 2 |
| #21797 | 89 |