Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
564 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 1. #26031559 | C2 | semidirect |
| 2. #26030343 | C2 | semidirect |
| 3. #26021051 | C2 | semidirect |
| 4. #26018864 | C2 | semidirect |
| 5. #26018863 | C2 | semidirect |
| 6. #26018121 | C2 | semidirect |
| 7. C89×#3109 | C2 | semidirect |
| 217. #3109 | D89 | semidirect |
| 222. C89 | #10026 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031559 | 2 |
| #26030343 | 2 |
| #26021051 | 2 |
| #26018864 | 2 |
| #26018863 | 2 |
| #26018121 | 2 |
| C89×#3109 | 2 |
| #10026 | 89 |