Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
464 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 93 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. #26020456 | C2 | semidirect |
| 4. #26020437 | C2 | semidirect |
| 6. #26018100 | C2 | semidirect |
| 7. C89×#1297 | C2 | semidirect |
| 24. #19151334 | C4 | semidirect |
| 25. #19151334 | C4 | semidirect |
| 26. #19151331 | C4 | semidirect |
| 27. #19151331 | C4 | semidirect |
| 223. #1297 | D89 | semidirect |
| 225. C89 | #8875 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029302 | 2 |
| #26020552 | 2 |
| #26020456 | 2 |
| #26020437 | 2 |
| #26018741 | 2 |
| #26018100 | 2 |
| C89×#1297 | 2 |
| #8875 | 89 |