Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
946 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 946 conjugacy classes of subgroups — too many to draw. Only its 163 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. #26034652 | C2 | semidirect |
| 2. #26031630 | C2 | semidirect |
| 3. #26019400 | C2 | semidirect |
| 4. #26019338 | C2 | semidirect |
| 5. #26018990 | C2 | semidirect |
| 6. #26018704 | C2 | semidirect |
| 7. C89×#3131 | C2 | semidirect |
| 172. #3131 | D89 | semidirect |
| 177. C89 | #18696 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26034652 | 2 |
| #26031630 | 2 |
| #26019400 | 2 |
| #26019338 | 2 |
| #26018990 | 2 |
| #26018704 | 2 |
| C89×#3131 | 2 |
| #18696 | 89 |