Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
654 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 654 conjugacy classes of subgroups — too many to draw. Only its 91 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. #26029308 | C2 | semidirect |
| 3. #26020218 | C2 | semidirect |
| 4. #26020201 | C2 | semidirect |
| 5. #26018382 | C2 | semidirect |
| 6. #26018372 | C2 | semidirect |
| 7. C89×#2120 | C2 | semidirect |
| 11. #19151787 | C4 | semidirect |
| 13. #19151784 | C4 | semidirect |
| 43. C2×#13083558 | D4 | semidirect |
| 44. C2×#13083558 | D4 | semidirect |
| 47. C22×#10623494 | D4 | semidirect |
| 48. C22×#10623494 | D4 | semidirect |
| 268. #2120 | D89 | semidirect |
| 273. C89 | #13045 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029643 | 2 |
| #26029308 | 2 |
| #26020218 | 2 |
| #26020201 | 2 |
| #26018382 | 2 |
| #26018372 | 2 |
| C89×#2120 | 2 |
| #13045 | 89 |