Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
510 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 510 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×#19151393 | C2 | semidirect |
| 3. #26018404 | C2 | direct (N × H) |
| 4. C2×#329×C89 | C2 | semidirect |
| 5. C2×#15668060 | C4 | semidirect |
| 9. #19151770 | C4 | semidirect |
| 12. C2×#15667931 | C4 | semidirect |
| 15. #19151393 | C22 | semidirect |
| 19. #329×C89 | C22 | semidirect |
| 23. #15668060 | C2×C4 | semidirect |
| 38. #15667931 | C2×C4 | semidirect |
| 175. C2×C89 | #1404 | semidirect |
| 180. C2×#329 | D89 | semidirect |
| 182. C89 | C2×#1404 | semidirect |
| 197. #329 | C2×D89 | semidirect |
| 353. C2 | #26018404 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151770 | 2 |
| C2×#19151393 | 2 |
| #26018404 | 2 |
| C2×#329×C89 | 2 |
| C2×#1404 | 89 |