Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
888 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 888 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. #26021080 | C2 | semidirect |
| 3. #26018987 | C2 | semidirect |
| 4. #26018985 | C2 | semidirect |
| 5. C89×#1962 | C2 | semidirect |
| 6. #19152340 | C4 | semidirect |
| 14. #19151622 | C22 | semidirect |
| 21. #423×C89 | C22 | semidirect |
| 23. C43×C89 | C22 | semidirect |
| 169. #1962 | D89 | semidirect |
| 172. C89 | #8530 | semidirect |
| 183. #423 | C2×D89 | semidirect |
| 186. C43 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26034657 | 2 |
| #26021080 | 2 |
| #26018987 | 2 |
| #26018985 | 2 |
| C89×#1962 | 2 |
| #8530 | 89 |