Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
282 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 65 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. #26022287 | C2 | semidirect |
| 2. #26019866 | C2 | semidirect |
| 3. #26019137 | C2 | semidirect |
| 4. #26018315 | C2 | semidirect |
| 5. #26018299 | C2 | semidirect |
| 6. #26018298 | C2 | semidirect |
| 7. C89×#2206 | C2 | semidirect |
| 104. #10623494 | D16 | semidirect |
| 129. #2206 | D89 | semidirect |
| 135. C89 | #12491 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022287 | 2 |
| #26019866 | 2 |
| #26019137 | 2 |
| #26018315 | 2 |
| #26018299 | 2 |
| #26018298 | 2 |
| C89×#2206 | 2 |
| #12491 | 89 |