Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
764 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 764 conjugacy classes of subgroups — too many to draw. Only its 81 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. #26028280 | C2 | semidirect |
| 3. #26020170 | C2 | semidirect |
| 4. #26018786 | C2 | semidirect |
| 5. #26018781 | C2 | semidirect |
| 6. #26018161 | C2 | semidirect |
| 263. C89 | #9981 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029512 | 2 |
| #26028280 | 2 |
| #26020170 | 2 |
| #26018786 | 2 |
| #26018781 | 2 |
| #26018161 | 2 |
| C89×#3006 | 2 |
| #9981 | 89 |