Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
894 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 894 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. #26029512 | C2 | semidirect |
| 2. #26025410 | C2 | semidirect |
| 3. #26020196 | C2 | semidirect |
| 4. #26018784 | C2 | semidirect |
| 5. #26018579 | C2 | semidirect |
| 6. #26018104 | C2 | semidirect |
| 33. C22×Dic178 | D4 | semidirect |
| 43. C2×C4⋊Dic89 | D4 | semidirect |
| 49. C2×C4×Dic89 | D4 | semidirect |
| 56. C22⋊#10623494 | D4 | semidirect |
| 281. C89 | #9942 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029512 | 2 |
| #26025410 | 2 |
| #26020196 | 2 |
| #26018784 | 2 |
| #26018579 | 2 |
| #26018104 | 2 |
| C89×#2404 | 2 |
| #9942 | 89 |