Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
770 conjugacy classes of subgroups; only the 255 normal subgroups are shown.
This group has 770 conjugacy classes of subgroups — too many to draw. Only its 255 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. #26020426 | C2 | semidirect |
| 4. #26020393 | C2 | semidirect |
| 6. #26020157 | C2 | semidirect |
| 7. C89×#1838 | C2 | semidirect |
| 112. #1838 | D89 | semidirect |
| 115. C89 | #20830 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028884 | 2 |
| C2×#97×D89 | 2 |
| #26020426 | 2 |
| #26020393 | 2 |
| #26020289 | 2 |
| #26020157 | 2 |
| C89×#1838 | 2 |
| #20830 | 89 |