Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
338 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 338 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 |
|---|---|---|
| 2. #26022438 | C2 | semidirect |
| 3. #26022433 | C2 | semidirect |
| 4. #26021692 | C2 | semidirect |
| 5. #26018268 | C2 | semidirect |
| 6. #26018268 | C2 | semidirect |
| 7. C89×#1315 | C2 | semidirect |
| 16. C2×#15667946 | C22 | semidirect |
| 23. #19151363 | C22 | semidirect |
| 25. C22⋊C16×C89 | C22 | semidirect |
| 26. C22⋊C16×C89 | C22 | semidirect |
| 170. #1315 | D89 | semidirect |
| 171. C89 | #12284 | semidirect |
| 187. C22⋊C16 | C2×D89 | semidirect |
| 188. C22⋊C16 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031117 | 2 |
| #26022438 | 2 |
| #26022433 | 2 |
| #26021692 | 2 |
| #26018268 | 2 |
| C89×#1315 | 2 |
| #12284 | 89 |