Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
844 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 844 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. C2×#19151385 | C2 | semidirect |
| 2. #26020244 | C2 | semidirect |
| 3. C4×#15667927 | C2 | semidirect |
| 12. C23×D4×C89 | C4 | semidirect |
| 19. #380×C89 | C4 | semidirect |
| 20. #379×C89 | C4 | semidirect |
| 28. #15667927 | D4 | semidirect |
| 194. C4×C89 | AΣL(1,𝔽16) | semidirect |
| 209. C89 | #13221 | semidirect |
| 210. C23×D4 | Dic89 | semidirect |
| 220. #380 | Dic89 | semidirect |
| 221. #379 | Dic89 | semidirect |
| 400. C4 | #19151385 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151385 | 2 |
| #26020244 | 2 |
| C4×#15667927 | 2 |
| C89×#2408 | 2 |
| #13221 | 89 |