Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1088 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 115 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. C22×#15667929 | C2 | semidirect |
| 2. C2×#19151385 | C2 | semidirect |
| 3. #26020167 | C2 | semidirect |
| 4. #26018370 | C2 | semidirect |
| 14. C23×D4×C89 | C4 | semidirect |
| 17. C2×#120×C89 | C4 | semidirect |
| 22. #386×C89 | C4 | semidirect |
| 24. #379×C89 | C4 | semidirect |
| 35. #15667929 | D4 | semidirect |
| 298. C22×C89 | AΣL(1,𝔽16) | semidirect |
| 327. C89 | #13082 | semidirect |
| 328. C23×D4 | Dic89 | semidirect |
| 332. C2×#120 | Dic89 | semidirect |
| 342. #386 | Dic89 | semidirect |
| 345. #379 | Dic89 | semidirect |
| 620. C22 | #19151385 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15667929 | 2 |
| C2×#19151385 | 2 |
| #26020167 | 2 |
| #26018370 | 2 |
| C89×#2403 | 2 |
| #13082 | 89 |