Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
960 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 960 conjugacy classes of subgroups — too many to draw. Only its 171 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. #26031239 | C2 | semidirect |
| 2. #26030655 | C2 | semidirect |
| 3. #26019575 | C2 | semidirect |
| 4. #26019545 | C2 | semidirect |
| 5. #26018879 | C2 | semidirect |
| 6. #26018850 | C2 | semidirect |
| 7. C2×#562×C89 | C2 | semidirect |
| 9. #19151988 | C22 | semidirect |
| 10. #19151968 | C22 | semidirect |
| 11. #19151964 | C22 | semidirect |
| 12. #19151957 | C22 | semidirect |
| 20. #19151340 | C22 | semidirect |
| 21. #19151338 | C22 | semidirect |
| 165. C2×#562 | D89 | semidirect |
| 172. C89 | #19001 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031239 | 2 |
| #26030655 | 2 |
| #26019575 | 2 |
| #26019545 | 2 |
| #26018879 | 2 |
| #26018850 | 2 |
| C2×#562×C89 | 2 |
| #19001 | 89 |