Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
618 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 618 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 |
|---|---|---|
| 1. #26029281 | C2 | semidirect |
| 3. #26018819 | C2 | semidirect |
| 4. #26018130 | C2 | semidirect |
| 5. C89×#1799 | C2 | semidirect |
| 12. #19151528 | C4 | semidirect |
| 13. #19151523 | C4 | semidirect |
| 14. #19151515 | C4 | semidirect |
| 15. #19151507 | C4 | semidirect |
| 44. C22⋊#10623494 | D4 | semidirect |
| 218. #1799 | D89 | semidirect |
| 221. C89 | #9386 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029281 | 2 |
| #26025208 | 2 |
| #26018819 | 2 |
| #26018130 | 2 |
| C89×#1799 | 2 |
| #9386 | 89 |