Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
682 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 682 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 3. #26020176 | C2 | semidirect |
| 5. #26018159 | C2 | semidirect |
| 6. #26018157 | C2 | semidirect |
| 7. C89×#1784 | C2 | semidirect |
| 176. C2×Dic89 | #101 | semidirect |
| 222. #1784 | D89 | semidirect |
| 226. C89 | #9506 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029291 | 2 |
| #26023611 | 2 |
| #26020176 | 2 |
| #26018588 | 2 |
| #26018159 | 2 |
| #26018157 | 2 |
| C89×#1784 | 2 |
| #9506 | 89 |