Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1220 conjugacy classes of subgroups; only the 271 normal subgroups are shown.
This group has 1220 conjugacy classes of subgroups — too many to draw. Only its 271 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. #26028716 | C2 | semidirect |
| 3. #26021923 | C2 | semidirect |
| 4. #26021915 | C2 | semidirect |
| 5. C89×#2884 | C2 | semidirect |
| 6. C2×#15668058 | C4 | semidirect |
| 11. #19152172 | C4 | semidirect |
| 14. C2×#15668001 | C4 | semidirect |
| 16. #41×Dic89 | C4 | semidirect |
| 18. #19151572 | C22 | semidirect |
| 19. #19151392 | C22 | semidirect |
| 20. #19151390 | C22 | semidirect |
| 24. #410×C89 | C22 | semidirect |
| 184. #2884 | D89 | semidirect |
| 187. C89 | #33362 | semidirect |
| 204. #410 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26034046 | 2 |
| #26028716 | 2 |
| #26021923 | 2 |
| #26021915 | 2 |
| C89×#2884 | 2 |
| #33362 | 89 |