Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1210 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 1210 conjugacy classes of subgroups — too many to draw. Only its 167 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. #26030193 | C2 | semidirect |
| 3. #26024539 | C2 | semidirect |
| 4. #26019291 | C2 | semidirect |
| 5. #26019257 | C2 | semidirect |
| 6. #26018782 | C2 | semidirect |
| 7. C89×#1463 | C2 | semidirect |
| 18. #19151917 | C22 | semidirect |
| 19. #19151912 | C22 | semidirect |
| 22. #19151537 | C22 | semidirect |
| 23. #19151528 | C22 | semidirect |
| 28. #19151333 | C22 | semidirect |
| 31. #324×C89 | C22 | semidirect |
| 215. #1463 | D89 | semidirect |
| 216. C89 | #18147 | semidirect |
| 240. #324 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152179 | 2 |
| #26030193 | 2 |
| #26024539 | 2 |
| #26019291 | 2 |
| #26019257 | 2 |
| #26018782 | 2 |
| C89×#1463 | 2 |
| #18147 | 89 |