Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
310 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 83 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. #26020371 | C2 | semidirect |
| 5. #26018147 | C2 | semidirect |
| 6. #26018080 | C2 | semidirect |
| 7. C89×#1301 | C2 | semidirect |
| 158. #1301 | D89 | semidirect |
| 160. C89 | #10629 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021083 | 2 |
| #26020371 | 2 |
| #26018902 | 2 |
| #26018899 | 2 |
| #26018147 | 2 |
| #26018080 | 2 |
| C89×#1301 | 2 |
| #10629 | 89 |