Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
376 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 73 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. #26021871 | C2 | semidirect |
| 3. #26020297 | C2 | semidirect |
| 4. #26018241 | C2 | semidirect |
| 5. #26018239 | C2 | semidirect |
| 6. #26018237 | C2 | semidirect |
| 7. C89×#1339 | C2 | semidirect |
| 8. C2×#15668031 | C4 | semidirect |
| 12. #19151857 | C4 | semidirect |
| 14. #19151848 | C4 | semidirect |
| 18. #106×D89 | C4 | semidirect |
| 190. #1339 | D89 | semidirect |
| 191. C89 | #11867 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029912 | 2 |
| #26021871 | 2 |
| #26020297 | 2 |
| #26018241 | 2 |
| #26018239 | 2 |
| #26018237 | 2 |
| C89×#1339 | 2 |
| #11867 | 89 |