Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
620 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 91 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. #26020326 | C2 | semidirect |
| 2. C2×#19151322 | C2 | semidirect |
| 3. #26018276 | C2 | semidirect |
| 4. #26018249 | C2 | semidirect |
| 13. C2×#121×C89 | C4 | semidirect |
| 16. #399×C89 | C4 | semidirect |
| 18. #392×C89 | C4 | semidirect |
| 22. C4×C22⋊C4×C89 | C4 | semidirect |
| 232. C89 | #11843 | semidirect |
| 234. C2×#121 | Dic89 | semidirect |
| 238. #399 | Dic89 | semidirect |
| 240. #392 | Dic89 | semidirect |
| 245. C4×C22⋊C4 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26020326 | 2 |
| C2×#19151322 | 2 |
| #26018276 | 2 |
| #26018249 | 2 |
| C89×#2539 | 2 |
| #11843 | 89 |