Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
514 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 514 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. #26020043 | C2 | semidirect |
| 3. #26018589 | C2 | semidirect |
| 4. #26018258 | C2 | semidirect |
| 5. #26018256 | C2 | semidirect |
| 6. #26018254 | C2 | semidirect |
| 7. C89×#1346 | C2 | semidirect |
| 220. #1346 | D89 | semidirect |
| 223. C89 | #11783 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26025213 | 2 |
| #26020043 | 2 |
| #26018589 | 2 |
| #26018258 | 2 |
| #26018256 | 2 |
| #26018254 | 2 |
| C89×#1346 | 2 |
| #11783 | 89 |