Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
770 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 770 conjugacy classes of subgroups — too many to draw. Only its 111 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. #26028697 | C2 | semidirect |
| 2. #26020170 | C2 | semidirect |
| 3. #26018781 | C2 | semidirect |
| 4. #26018105 | C2 | semidirect |
| 15. C2×#127×C89 | C4 | semidirect |
| 16. C2×#124×C89 | C4 | semidirect |
| 20. #391×C89 | C4 | semidirect |
| 21. #390×C89 | C4 | semidirect |
| 35. C22⋊#10623494 | D4 | semidirect |
| 252. C89 | #9445 | semidirect |
| 255. C2×#127 | Dic89 | semidirect |
| 256. C2×#124 | Dic89 | semidirect |
| 265. #391 | Dic89 | semidirect |
| 266. #390 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028697 | 2 |
| #26020170 | 2 |
| #26018781 | 2 |
| #26018105 | 2 |
| C89×#2431 | 2 |
| #9445 | 89 |