Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
400 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 400 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 |
|---|---|---|
| 4. #26018878 | C2 | semidirect |
| 5. #26018607 | C2 | semidirect |
| 6. #26018164 | C2 | semidirect |
| 7. C89×#1287 | C2 | semidirect |
| 158. #1287 | D89 | semidirect |
| 159. C89 | #9335 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031444 | 2 |
| #26029322 | 2 |
| #26018955 | 2 |
| #26018878 | 2 |
| #26018607 | 2 |
| #26018164 | 2 |
| C89×#1287 | 2 |
| #9335 | 89 |