Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
178 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 178 conjugacy classes of subgroups — too many to draw. Only its 59 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. #26022036 | C2 | semidirect |
| 3. #26018454 | C2 | semidirect |
| 4. #26018452 | C2 | semidirect |
| 5. #26018431 | C2 | semidirect |
| 6. #26018431 | C2 | semidirect |
| 7. C89×C22⋊C32 | C2 | semidirect |
| 94. C22⋊C32 | D89 | semidirect |
| 95. C89 | #13713 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022338 | 2 |
| #26022036 | 2 |
| #26018454 | 2 |
| #26018452 | 2 |
| #26018431 | 2 |
| C89×C22⋊C32 | 2 |
| #13713 | 89 |