Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
476 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 63 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. #26022171 | C2 | semidirect |
| 3. #26022168 | C2 | semidirect |
| 4. #26021263 | C2 | semidirect |
| 5. #26018260 | C2 | semidirect |
| 6. #26018175 | C2 | semidirect |
| 7. C89×#1347 | C2 | semidirect |
| 8. C22×Dic356 | C22 | semidirect |
| 23. C22⋊#13083549 | C22 | semidirect |
| 25. C22⋊C16×C89 | C22 | semidirect |
| 26. #340×C89 | C22 | semidirect |
| 129. C22×D89 | SD32 | semidirect |
| 205. #1347 | D89 | semidirect |
| 207. C89 | #12105 | semidirect |
| 225. C22⋊C16 | C2×D89 | semidirect |
| 226. #340 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030999 | 2 |
| #26022171 | 2 |
| #26022168 | 2 |
| #26021263 | 2 |
| #26018260 | 2 |
| #26018175 | 2 |
| C89×#1347 | 2 |
| #12105 | 89 |