Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
438 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 71 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. #26020331 | C2 | semidirect |
| 3. #324×D89 | C2 | semidirect |
| 4. #26018280 | C2 | semidirect |
| 5. #26018278 | C2 | semidirect |
| 6. #26018255 | C2 | semidirect |
| 7. C89×#1345 | C2 | semidirect |
| 210. #1345 | D89 | semidirect |
| 211. C89 | #11852 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26025726 | 2 |
| #26020331 | 2 |
| #324×D89 | 2 |
| #26018280 | 2 |
| #26018278 | 2 |
| #26018255 | 2 |
| C89×#1345 | 2 |
| #11852 | 89 |