Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
340 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 79 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. #26022502 | C2 | semidirect |
| 2. #26022501 | C2 | semidirect |
| 3. #26022477 | C2 | semidirect |
| 4. #26019866 | C2 | semidirect |
| 5. #26019845 | C2 | semidirect |
| 6. #26018171 | C2 | semidirect |
| 7. C89×#2240 | C2 | semidirect |
| 97. #10623494 | D16 | semidirect |
| 123. #2240 | D89 | semidirect |
| 127. C89 | #12525 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022502 | 2 |
| #26022501 | 2 |
| #26022477 | 2 |
| #26019866 | 2 |
| #26019845 | 2 |
| #26018171 | 2 |
| C89×#2240 | 2 |
| #12525 | 89 |