Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
730 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 730 conjugacy classes of subgroups — too many to draw. Only its 117 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. #26029275 | C2 | semidirect |
| 3. #26020241 | C2 | semidirect |
| 4. #26018921 | C2 | semidirect |
| 5. #26018919 | C2 | semidirect |
| 6. #26018155 | C2 | semidirect |
| 7. C89×#1303 | C2 | semidirect |
| 50. C4⋊#10623494 | D4 | semidirect |
| 61. C4⋊C8×C89 | D4 | semidirect |
| 203. #1303 | D89 | semidirect |
| 204. C89 | #9397 | semidirect |
| 254. C4⋊C8 | D356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029275 | 2 |
| #26025194 | 2 |
| #26020241 | 2 |
| #26018921 | 2 |
| #26018919 | 2 |
| #26018155 | 2 |
| C89×#1303 | 2 |
| #9397 | 89 |