Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
432 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 432 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 |
|---|---|---|
| 2. #349×D89 | C2 | semidirect |
| 3. #338×D89 | C2 | semidirect |
| 4. #26018246 | C2 | semidirect |
| 5. #26018244 | C2 | semidirect |
| 6. #26018242 | C2 | semidirect |
| 7. C89×#1342 | C2 | semidirect |
| 206. #1342 | D89 | semidirect |
| 209. C89 | #11688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029863 | 2 |
| #349×D89 | 2 |
| #338×D89 | 2 |
| #26018246 | 2 |
| #26018244 | 2 |
| #26018242 | 2 |
| C89×#1342 | 2 |
| #11688 | 89 |