Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
472 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 91 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. #26029270 | C2 | semidirect |
| 3. #26018849 | C2 | semidirect |
| 4. #26018687 | C2 | semidirect |
| 5. #26018603 | C2 | semidirect |
| 6. #26018163 | C2 | semidirect |
| 7. C89×#1299 | C2 | semidirect |
| 214. #1299 | D89 | semidirect |
| 215. C89 | #9350 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029747 | 2 |
| #26029270 | 2 |
| #26018849 | 2 |
| #26018687 | 2 |
| #26018603 | 2 |
| #26018163 | 2 |
| C89×#1299 | 2 |
| #9350 | 89 |