Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
514 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 75 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×#19151338 | C2 | semidirect |
| 3. #26018399 | C2 | direct (N × H) |
| 4. C2×#355×C89 | C2 | semidirect |
| 15. #19151338 | C22 | semidirect |
| 19. #355×C89 | C22 | semidirect |
| 176. C2×C89 | #1403 | semidirect |
| 180. C2×#355 | D89 | semidirect |
| 183. C89 | C2×#1403 | semidirect |
| 196. #355 | C2×D89 | semidirect |
| 355. C2 | #26018399 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151775 | 2 |
| C2×#19151338 | 2 |
| #26018399 | 2 |
| C2×#355×C89 | 2 |
| C2×#1403 | 89 |