Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
652 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 652 conjugacy classes of subgroups — too many to draw. Only its 111 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. #26021207 | C2 | semidirect |
| 3. #26021197 | C2 | semidirect |
| 4. #26018855 | C2 | semidirect |
| 7. C89×#1552 | C2 | semidirect |
| 8. C89⋊#564 | C4 | semidirect |
| 9. #19152352 | C4 | semidirect |
| 250. #1552 | D89 | semidirect |
| 254. C89 | #8512 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26034862 | 2 |
| #26021207 | 2 |
| #26021197 | 2 |
| #26018855 | 2 |
| #26018778 | 2 |
| #26018663 | 2 |
| C89×#1552 | 2 |
| #8512 | 89 |