Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
380 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 93 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. #26020406 | C2 | semidirect |
| 3. #26019038 | C2 | semidirect |
| 6. #26018103 | C2 | semidirect |
| 7. C89×#1300 | C2 | semidirect |
| 185. #1300 | D89 | semidirect |
| 187. C89 | #8876 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029393 | 2 |
| #26020406 | 2 |
| #26019038 | 2 |
| #26018736 | 2 |
| #26018666 | 2 |
| #26018103 | 2 |
| C89×#1300 | 2 |
| #8876 | 89 |