Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
496 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 107 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×#19151355 | C2 | semidirect |
| 3. #26018238 | C2 | direct (N × H) |
| 4. C2×#349×C89 | C2 | semidirect |
| 5. C22×D712 | C4 | semidirect |
| 10. #19151851 | C4 | semidirect |
| 12. C2×#15667944 | C4 | semidirect |
| 15. #19151355 | C22 | semidirect |
| 19. #349×C89 | C22 | semidirect |
| 25. C2×D712 | C2×C4 | semidirect |
| 40. #15667944 | C2×C4 | semidirect |
| 174. C2×C89 | #1339 | semidirect |
| 178. C2×#349 | D89 | semidirect |
| 181. C89 | C2×#1339 | semidirect |
| 194. #349 | C2×D89 | semidirect |
| 351. C2 | #26018238 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151851 | 2 |
| C2×#19151355 | 2 |
| #26018238 | 2 |
| C2×#349×C89 | 2 |
| C2×#1339 | 89 |