Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
896 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 896 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. #26031267 | C2 | semidirect |
| 2. #26030628 | C2 | semidirect |
| 3. #26019554 | C2 | semidirect |
| 4. #26019550 | C2 | semidirect |
| 5. #26019545 | C2 | semidirect |
| 6. #26018890 | C2 | semidirect |
| 7. #26018859 | C2 | semidirect |
| 8. C89×#3531 | C2 | semidirect |
| 22. #19151340 | C22 | semidirect |
| 23. #19151340 | C22 | semidirect |
| 24. #19151340 | C22 | semidirect |
| 25. #19151338 | C22 | semidirect |
| 26. #564×C89 | C22 | semidirect |
| 29. #563×C89 | C22 | semidirect |
| 31. #562×C89 | C22 | semidirect |
| 212. #3531 | D89 | semidirect |
| 220. C89 | #19004 | semidirect |
| 221. #564 | C2×D89 | semidirect |
| 224. #563 | C2×D89 | semidirect |
| 226. #562 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031267 | 2 |
| #26030628 | 2 |
| #26019554 | 2 |
| #26019550 | 2 |
| #26019545 | 2 |
| #26018890 | 2 |
| #26018859 | 2 |
| C89×#3531 | 2 |
| #19004 | 89 |