Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
392 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 3. #26019017 | C2 | semidirect |
| 5. #26018146 | C2 | semidirect |
| 6. #26018144 | C2 | semidirect |
| 7. C89×#1569 | C2 | semidirect |
| 22. #19151337 | C4 | semidirect |
| 23. #19151337 | C4 | semidirect |
| 24. #19151337 | C4 | semidirect |
| 25. #19151337 | C4 | semidirect |
| 190. #1569 | D89 | semidirect |
| 194. C89 | #8918 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029322 | 2 |
| #26021083 | 2 |
| #26019017 | 2 |
| #26018843 | 2 |
| #26018146 | 2 |
| #26018144 | 2 |
| C89×#1569 | 2 |
| #8918 | 89 |