Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
516 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 89 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. #26028887 | C2 | semidirect |
| 3. #26020327 | C2 | semidirect |
| 6. #26018105 | C2 | semidirect |
| 7. C89×#1284 | C2 | semidirect |
| 17. #19151500 | C4 | semidirect |
| 18. #19151500 | C4 | semidirect |
| 21. #19151468 | C4 | semidirect |
| 22. #19151464 | C4 | semidirect |
| 242. #1284 | D89 | semidirect |
| 243. C89 | #9446 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028887 | 2 |
| #26024714 | 2 |
| #26020327 | 2 |
| #26018782 | 2 |
| #26018780 | 2 |
| #26018105 | 2 |
| C89×#1284 | 2 |
| #9446 | 89 |