Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
530 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 530 conjugacy classes of subgroups — too many to draw. Only its 97 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. #26029318 | C2 | semidirect |
| 3. #26018843 | C2 | semidirect |
| 4. #26018670 | C2 | semidirect |
| 5. #26018668 | C2 | semidirect |
| 6. #26018089 | C2 | semidirect |
| 7. C89×#1278 | C2 | semidirect |
| 204. #1278 | D89 | semidirect |
| 205. C89 | #9069 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030680 | 2 |
| #26029318 | 2 |
| #26018843 | 2 |
| #26018670 | 2 |
| #26018668 | 2 |
| #26018089 | 2 |
| C89×#1278 | 2 |
| #9069 | 89 |