Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
500 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 81 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. #26030374 | C2 | semidirect |
| 3. #26018887 | C2 | semidirect |
| 4. #26018722 | C2 | semidirect |
| 5. #26018596 | C2 | semidirect |
| 6. #26018114 | C2 | semidirect |
| 7. C89×#3103 | C2 | semidirect |
| 199. #3103 | D89 | semidirect |
| 204. C89 | #10040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031243 | 2 |
| #26030374 | 2 |
| #26018887 | 2 |
| #26018722 | 2 |
| #26018596 | 2 |
| #26018114 | 2 |
| C89×#3103 | 2 |
| #10040 | 89 |