Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
542 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 131 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. #26020248 | C2 | semidirect |
| 4. #26018111 | C2 | semidirect |
| 5. C89×#2982 | C2 | semidirect |
| 152. #2982 | D89 | semidirect |
| 157. C89 | #9486 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26025157 | 2 |
| #26020248 | 2 |
| #26018678 | 2 |
| #26018111 | 2 |
| C89×#2982 | 2 |
| #9486 | 89 |