Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
434 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 434 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. #26021943 | C2 | semidirect |
| 3. #26020800 | C2 | semidirect |
| 4. #26020797 | C2 | semidirect |
| 5. #26020474 | C2 | semidirect |
| 6. #26018374 | C2 | semidirect |
| 7. C89×#2134 | C2 | semidirect |
| 202. #2134 | D89 | semidirect |
| 207. C89 | #13429 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031113 | 2 |
| #26021943 | 2 |
| #26020800 | 2 |
| #26020797 | 2 |
| #26020474 | 2 |
| #26018374 | 2 |
| C89×#2134 | 2 |
| #13429 | 89 |