Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
372 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 71 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. #26022488 | C2 | semidirect |
| 2. #26022399 | C2 | semidirect |
| 3. #26019765 | C2 | semidirect |
| 4. #26018295 | C2 | semidirect |
| 5. #26018219 | C2 | semidirect |
| 6. #26018210 | C2 | semidirect |
| 8. #19152003 | C22 | semidirect |
| 11. C4⋊#13083549 | C22 | semidirect |
| 15. #19151374 | C22 | semidirect |
| 16. #19151349 | C22 | semidirect |
| 91. D8×C89 | SD16 | semidirect |
| 174. C89 | #12378 | semidirect |
| 253. D8 | #13083562 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022488 | 2 |
| #26022399 | 2 |
| #26019765 | 2 |
| #26018295 | 2 |
| #26018219 | 2 |
| #26018210 | 2 |
| C89×#3273 | 2 |
| #12378 | 89 |