Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
434 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 99 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. #26020302 | C2 | semidirect |
| 4. #26018380 | C2 | semidirect |
| 5. C89×#1812 | C2 | semidirect |
| 6. C22×C8×D89 | C4 | semidirect |
| 13. #19151626 | C4 | semidirect |
| 16. #19151561 | C4 | semidirect |
| 17. #19151553 | C4 | semidirect |
| 190. #1812 | D89 | semidirect |
| 192. C89 | #12805 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028944 | 2 |
| #26021891 | 2 |
| #26020302 | 2 |
| #26018380 | 2 |
| C89×#1812 | 2 |
| #12805 | 89 |