Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
288 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 63 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. #26022564 | C2 | semidirect |
| 2. C2×#19151433 | C2 | semidirect |
| 3. #26022372 | C2 | semidirect |
| 4. #26018442 | C2 | semidirect |
| 5. #26018436 | C2 | semidirect |
| 6. #26018394 | C2 | semidirect |
| 7. C89×#3415 | C2 | semidirect |
| 8. C2×D1424 | C22 | semidirect |
| 13. #19151432 | C22 | semidirect |
| 14. C2×#15667918 | C22 | semidirect |
| 15. #19151428 | C22 | semidirect |
| 122. #3415 | D89 | semidirect |
| 129. C89 | #13669 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022564 | 2 |
| C2×#19151433 | 2 |
| #26022372 | 2 |
| #26018442 | 2 |
| #26018436 | 2 |
| #26018394 | 2 |
| C89×#3415 | 2 |
| #13669 | 89 |