Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
714 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 714 conjugacy classes of subgroups — too many to draw. Only its 171 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 |
|---|---|---|
| 1. C2×#19152014 | C2 | semidirect |
| 2. #26029896 | C2 | semidirect |
| 3. #26022352 | C2 | semidirect |
| 4. #26022335 | C2 | semidirect |
| 5. #26022036 | C2 | semidirect |
| 6. #26021968 | C2 | semidirect |
| 7. C22×D16×C89 | C2 | semidirect |
| 12. C2×#15667951 | C22 | semidirect |
| 13. C2×C16×D89 | C22 | semidirect |
| 15. #19151831 | C22 | semidirect |
| 18. #19151426 | C22 | semidirect |
| 19. #19151424 | C22 | semidirect |
| 20. #19151399 | C22 | semidirect |
| 52. C2×C16×C89 | D4 | semidirect |
| 130. C22×D16 | D89 | semidirect |
| 137. C89 | #33607 | semidirect |
| 179. C2×C16 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152014 | 2 |
| #26029896 | 2 |
| #26022352 | 2 |
| #26022335 | 2 |
| #26022036 | 2 |
| #26021968 | 2 |
| C22×D16×C89 | 2 |
| #33607 | 89 |