Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
496 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 71 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. C2×#19151395 | C2 | semidirect |
| 3. #26018401 | C2 | semidirect |
| 4. C89×#1533 | C2 | semidirect |
| 15. #19151395 | C22 | semidirect |
| 19. #329×C89 | C22 | semidirect |
| 180. #1533 | D89 | semidirect |
| 182. C89 | #13565 | semidirect |
| 197. #329 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151775 | 2 |
| C2×#19151395 | 2 |
| #26018401 | 2 |
| C89×#1533 | 2 |
| #13565 | 89 |