Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1312 conjugacy classes of subgroups; only the 271 normal subgroups are shown.
This group has 1312 conjugacy classes of subgroups — too many to draw. Only its 271 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. #26028731 | C2 | semidirect |
| 3. #26021943 | C2 | semidirect |
| 4. #26021935 | C2 | semidirect |
| 5. C89×#2888 | C2 | semidirect |
| 17. #19151582 | C22 | semidirect |
| 19. #19151396 | C22 | semidirect |
| 20. #19151394 | C22 | semidirect |
| 23. #413×C89 | C22 | semidirect |
| 187. #2888 | D89 | semidirect |
| 190. C89 | #33373 | semidirect |
| 205. #413 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26034026 | 2 |
| #26028731 | 2 |
| #26021943 | 2 |
| #26021935 | 2 |
| C89×#2888 | 2 |
| #33373 | 89 |