Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
500 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 83 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. #26018570 | C2 | semidirect |
| 3. #26018272 | C2 | semidirect |
| 4. #26018248 | C2 | semidirect |
| 5. C4×#99×C89 | C2 | semidirect |
| 6. C2×#15668000 | C4 | semidirect |
| 9. #19151510 | C4 | semidirect |
| 11. #19151507 | C4 | semidirect |
| 16. #19151466 | C4 | semidirect |
| 199. C4×#99 | D89 | semidirect |
| 203. C89 | #11730 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26026104 | 2 |
| #26018570 | 2 |
| #26018272 | 2 |
| #26018248 | 2 |
| C4×#99×C89 | 2 |
| #11730 | 89 |