Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
396 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 2. #26022437 | C2 | semidirect |
| 3. #26021681 | C2 | semidirect |
| 4. #26018262 | C2 | semidirect |
| 5. #26018261 | C2 | semidirect |
| 6. #26018175 | C2 | semidirect |
| 7. C89×#2233 | C2 | semidirect |
| 19. C22⋊#13083549 | C22 | semidirect |
| 20. #19151361 | C22 | semidirect |
| 23. C2×#107×C89 | C22 | semidirect |
| 26. C22⋊C16×C89 | C22 | semidirect |
| 183. #2233 | D89 | semidirect |
| 188. C89 | #12281 | semidirect |
| 197. C2×#107 | C2×D89 | semidirect |
| 205. C22⋊C16 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030999 | 2 |
| #26022437 | 2 |
| #26021681 | 2 |
| #26018262 | 2 |
| #26018261 | 2 |
| #26018175 | 2 |
| C89×#2233 | 2 |
| #12281 | 89 |