Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
274 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 274 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 |
|---|---|---|
| 1. #26022469 | C2 | semidirect |
| 3. #26021832 | C2 | semidirect |
| 4. #26018246 | C2 | semidirect |
| 6. #26018205 | C2 | semidirect |
| 144. C89 | #12306 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022469 | 2 |
| #26022464 | 2 |
| #26021832 | 2 |
| #26018246 | 2 |
| #26018243 | 2 |
| #26018205 | 2 |
| C89×#3263 | 2 |
| #12306 | 89 |