Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
834 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 834 conjugacy classes of subgroups — too many to draw. Only its 131 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×#19151324 | C2 | semidirect |
| 3. #26018183 | C2 | direct (N × H) |
| 4. C2×#324×C89 | C2 | semidirect |
| 15. #19151324 | C22 | semidirect |
| 19. #324×C89 | C22 | semidirect |
| 26. C22×D356 | C8 | semidirect |
| 72. C2×D356 | C2×C8 | semidirect |
| 199. C2×C89 | #1318 | semidirect |
| 206. C2×#324 | D89 | semidirect |
| 208. C89 | C2×#1318 | semidirect |
| 223. #324 | C2×D89 | semidirect |
| 403. C2 | #26018183 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151499 | 2 |
| C2×#19151324 | 2 |
| #26018183 | 2 |
| C2×#324×C89 | 2 |
| C2×#1318 | 89 |