Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
376 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 107 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. #26019026 | C2 | semidirect |
| 5. #26018149 | C2 | semidirect |
| 6. #26018085 | C2 | semidirect |
| 7. C4×C4⋊C8×C89 | C2 | semidirect |
| 15. #19151345 | C4 | semidirect |
| 16. #19151341 | C4 | semidirect |
| 157. C4×C4⋊C8 | D89 | semidirect |
| 163. C89 | #9577 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021080 | 2 |
| #26019026 | 2 |
| #26018902 | 2 |
| #26018650 | 2 |
| #26018149 | 2 |
| #26018085 | 2 |
| C4×C4⋊C8×C89 | 2 |
| #9577 | 89 |