Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
720 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 720 conjugacy classes of subgroups — too many to draw. Only its 103 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. #26018767 | C2 | semidirect |
| 3. #26018579 | C2 | semidirect |
| 4. #26018138 | C2 | semidirect |
| 5. C89×#2312 | C2 | semidirect |
| 10. #19151534 | C4 | semidirect |
| 11. #19151507 | C4 | semidirect |
| 52. #95×C89 | D4 | semidirect |
| 184. #2312 | D89 | semidirect |
| 188. C89 | #9413 | semidirect |
| 235. #95 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26025183 | 2 |
| #26018767 | 2 |
| #26018579 | 2 |
| #26018138 | 2 |
| C89×#2312 | 2 |
| #9413 | 89 |