Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1064 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 1064 conjugacy classes of subgroups — too many to draw. Only its 187 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. #26031024 | C2 | semidirect |
| 3. #26019276 | C2 | semidirect |
| 4. #26019208 | C2 | semidirect |
| 5. #26018823 | C2 | semidirect |
| 16. #19151933 | C22 | semidirect |
| 19. #19151754 | C22 | semidirect |
| 22. #19151334 | C22 | semidirect |
| 109. C24×C89 | Q16 | semidirect |
| 229. C89 | #18287 | semidirect |
| 308. C24 | #13083564 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152224 | 2 |
| #26031024 | 2 |
| #26019276 | 2 |
| #26019208 | 2 |
| #26018823 | 2 |
| C2×#19151322 | 2 |
| C89×#2626 | 2 |
| #18287 | 89 |