Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
338 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 2. #26020393 | C2 | semidirect |
| 3. #26019020 | C2 | semidirect |
| 6. #26018143 | C2 | semidirect |
| 7. C89×#1302 | C2 | semidirect |
| 171. #1302 | D89 | semidirect |
| 173. C89 | #8917 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029424 | 2 |
| #26020393 | 2 |
| #26019020 | 2 |
| #26018838 | 2 |
| #26018718 | 2 |
| #26018143 | 2 |
| C89×#1302 | 2 |
| #8917 | 89 |