Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
434 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 434 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. #26021943 | C2 | semidirect |
| 3. #26020799 | C2 | semidirect |
| 4. #26018375 | C2 | semidirect |
| 5. C89×#1858 | C2 | semidirect |
| 134. #1858 | D89 | semidirect |
| 136. C89 | #13429 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031117 | 2 |
| #26021943 | 2 |
| #26020799 | 2 |
| #26018375 | 2 |
| C89×#1858 | 2 |
| #13429 | 89 |