Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
556 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 109 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. #26020342 | C2 | semidirect |
| 5. #26018120 | C2 | semidirect |
| 6. #26018119 | C2 | semidirect |
| 7. C89×#1824 | C2 | semidirect |
| 15. #19151536 | C4 | semidirect |
| 16. #19151533 | C4 | semidirect |
| 227. #1824 | D89 | semidirect |
| 231. C89 | #9473 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029278 | 2 |
| #26024563 | 2 |
| #26020342 | 2 |
| #26020237 | 2 |
| #26018120 | 2 |
| #26018119 | 2 |
| C89×#1824 | 2 |
| #9473 | 89 |