Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
324 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 79 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. #26022064 | C2 | semidirect |
| 2. #26020401 | C2 | semidirect |
| 3. #26018243 | C2 | semidirect |
| 4. #26018237 | C2 | semidirect |
| 14. #498×C89 | C4 | semidirect |
| 15. #493×C89 | C4 | semidirect |
| 20. #442×C89 | C4 | semidirect |
| 123. C89 | #11837 | semidirect |
| 125. #498 | Dic89 | semidirect |
| 126. #493 | Dic89 | semidirect |
| 131. #442 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022064 | 2 |
| #26020401 | 2 |
| #26018243 | 2 |
| #26018237 | 2 |
| C89×#3184 | 2 |
| #11837 | 89 |