Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
768 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 768 conjugacy classes of subgroups — too many to draw. Only its 85 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. #26030188 | C2 | semidirect |
| 2. #26024526 | C2 | semidirect |
| 3. #26020352 | C2 | semidirect |
| 4. #26018781 | C2 | semidirect |
| 5. #26018579 | C2 | semidirect |
| 6. #26018105 | C2 | semidirect |
| 39. C2×C4⋊Dic89 | D4 | semidirect |
| 40. C2×C4⋊Dic89 | D4 | semidirect |
| 54. C22⋊#10623494 | D4 | semidirect |
| 57. #15667919 | D4 | semidirect |
| 257. C89 | #9940 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030188 | 2 |
| #26024526 | 2 |
| #26020352 | 2 |
| #26018781 | 2 |
| #26018579 | 2 |
| #26018105 | 2 |
| C89×#2539 | 2 |
| #9940 | 89 |