Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
418 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 69 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. #26022396 | C2 | semidirect |
| 3. #26019648 | C2 | semidirect |
| 4. #26018298 | C2 | semidirect |
| 5. #26018214 | C2 | semidirect |
| 6. #26018208 | C2 | semidirect |
| 7. C89×#2240 | C2 | semidirect |
| 17. C4⋊#13083549 | C22 | semidirect |
| 19. #19151351 | C22 | semidirect |
| 21. #500×C89 | C22 | semidirect |
| 24. C4×C16×C89 | C22 | semidirect |
| 151. #2240 | D89 | semidirect |
| 157. C89 | #12372 | semidirect |
| 160. #500 | C2×D89 | semidirect |
| 172. C4×C16 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031927 | 2 |
| #26022396 | 2 |
| #26019648 | 2 |
| #26018298 | 2 |
| #26018214 | 2 |
| #26018208 | 2 |
| C89×#2240 | 2 |
| #12372 | 89 |