Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1022 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 1022 conjugacy classes of subgroups — too many to draw. Only its 251 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×#15667953 | C2 | semidirect |
| 2. C2×#19151975 | C2 | semidirect |
| 3. #26022501 | C2 | direct (N × H) |
| 4. C2×C4×#13083549 | C2 | semidirect |
| 5. C2×#493×C89 | C2 | semidirect |
| 10. C2×#15667953 | C22 | semidirect |
| 13. #19151975 | C22 | semidirect |
| 14. C4×#13083549 | C22 | semidirect |
| 19. #493×C89 | C22 | semidirect |
| 31. C2×#13083549 | D4 | semidirect |
| 57. #13083549 | C2×D4 | semidirect |
| 88. C2×C4×C89 | D16 | semidirect |
| 111. C4×C89 | C2×D16 | semidirect |
| 116. C2×C89 | #2246 | semidirect |
| 122. C2×#493 | D89 | semidirect |
| 125. C89 | C2×#2246 | semidirect |
| 138. #493 | C2×D89 | semidirect |
| 212. C2×C4 | #15667953 | semidirect |
| 231. C4 | C2×#15667953 | semidirect |
| 236. C2 | #26022501 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15667953 | 2 |
| C2×#19151975 | 2 |
| #26022501 | 2 |
| C2×C4×#13083549 | 2 |
| C2×#493×C89 | 2 |
| C2×#2246 | 89 |