Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
508 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 103 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. #26023433 | C2 | semidirect |
| 2. #26018978 | C2 | semidirect |
| 4. #26018117 | C2 | semidirect |
| 16. #494×C89 | C4 | semidirect |
| 17. #492×C89 | C4 | semidirect |
| 122. C89 | #9429 | semidirect |
| 127. #494 | Dic89 | semidirect |
| 128. #492 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023433 | 2 |
| #26018978 | 2 |
| #26018799 | 2 |
| #26018117 | 2 |
| C89×#3152 | 2 |
| #9429 | 89 |