Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
324 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 71 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. #26022064 | C2 | semidirect |
| 3. #26018242 | C2 | semidirect |
| 4. #26018236 | C2 | semidirect |
| 5. C89×#1841 | C2 | semidirect |
| 7. #19151996 | C4 | semidirect |
| 8. #19151975 | C4 | semidirect |
| 13. #19151711 | C4 | semidirect |
| 120. #1841 | D89 | semidirect |
| 123. C89 | #11837 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030990 | 2 |
| #26022064 | 2 |
| #26018242 | 2 |
| #26018236 | 2 |
| C89×#1841 | 2 |
| #11837 | 89 |