Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
732 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 115 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. #26021238 | C2 | semidirect |
| 4. #26018772 | C2 | semidirect |
| 5. #26018157 | C2 | semidirect |
| 6. #26018137 | C2 | semidirect |
| 22. C2×#137×C89 | C4 | semidirect |
| 27. #417×C89 | C4 | semidirect |
| 233. C89 | #9364 | semidirect |
| 235. C2×#137 | Dic89 | semidirect |
| 242. #417 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023093 | 2 |
| #26021238 | 2 |
| #26020196 | 2 |
| #26018772 | 2 |
| #26018157 | 2 |
| #26018137 | 2 |
| C89×#3007 | 2 |
| #9364 | 89 |