Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
368 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 99 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. #26021873 | C2 | semidirect |
| 3. #26018204 | C2 | semidirect |
| 4. #26018187 | C2 | semidirect |
| 5. C89×#2115 | C2 | semidirect |
| 175. #2115 | D89 | semidirect |
| 178. C89 | #11484 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028953 | 2 |
| #26021873 | 2 |
| #26018204 | 2 |
| #26018187 | 2 |
| C89×#2115 | 2 |
| #11484 | 89 |