Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
628 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 628 conjugacy classes of subgroups — too many to draw. Only its 85 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. #26026198 | C2 | semidirect |
| 3. #26018965 | C2 | semidirect |
| 4. #26018854 | C2 | semidirect |
| 5. #26018760 | C2 | semidirect |
| 6. #26018144 | C2 | semidirect |
| 7. C89×#3234 | C2 | semidirect |
| 190. #3234 | D89 | semidirect |
| 197. C89 | #10089 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030705 | 2 |
| #26026198 | 2 |
| #26018965 | 2 |
| #26018854 | 2 |
| #26018760 | 2 |
| #26018144 | 2 |
| C89×#3234 | 2 |
| #10089 | 89 |