Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
288 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 59 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. #26033393 | C2 | semidirect |
| 2. #26022565 | C2 | semidirect |
| 3. C2×#19151433 | C2 | semidirect |
| 4. #26018441 | C2 | semidirect |
| 5. #26018435 | C2 | semidirect |
| 6. #26018394 | C2 | semidirect |
| 7. C89×#2221 | C2 | semidirect |
| 18. #19151432 | C22 | semidirect |
| 19. C2×#15667918 | C22 | semidirect |
| 20. C2×D16×C89 | C22 | semidirect |
| 23. #368×C89 | C22 | semidirect |
| 125. #2221 | D89 | semidirect |
| 129. C89 | #13669 | semidirect |
| 137. C2×D16 | C2×D89 | semidirect |
| 145. #368 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033393 | 2 |
| #26022565 | 2 |
| C2×#19151433 | 2 |
| #26018441 | 2 |
| #26018435 | 2 |
| #26018394 | 2 |
| C89×#2221 | 2 |
| #13669 | 89 |