Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
800 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 800 conjugacy classes of subgroups — too many to draw. Only its 139 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. #26021230 | C2 | semidirect |
| 2. #26021081 | C2 | semidirect |
| 3. #26018990 | C2 | semidirect |
| 4. #26018987 | C2 | semidirect |
| 14. #562×C89 | C4 | semidirect |
| 147. C89 | #8532 | semidirect |
| 148. #562 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021230 | 2 |
| #26021081 | 2 |
| #26018990 | 2 |
| #26018987 | 2 |
| C89×#3548 | 2 |
| #8532 | 89 |