Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
540 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 1. #26030653 | C2 | semidirect |
| 3. #26026123 | C2 | semidirect |
| 4. #26018878 | C2 | semidirect |
| 5. #26018798 | C2 | semidirect |
| 6. #26018696 | C2 | semidirect |
| 7. C89×#1288 | C2 | semidirect |
| 209. #1288 | D89 | semidirect |
| 210. C89 | #10019 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030653 | 2 |
| #26030344 | 2 |
| #26026123 | 2 |
| #26018878 | 2 |
| #26018798 | 2 |
| #26018696 | 2 |
| C89×#1288 | 2 |
| #10019 | 89 |