Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
356 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 17. #19151344 | C4 | semidirect |
| 18. #19151344 | C4 | semidirect |
| 19. #19151344 | C4 | semidirect |
| 20. #19151344 | C4 | semidirect |
| 157. C89 | #8936 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021230 | 2 |
| #26019040 | 2 |
| #26018917 | 2 |
| #26018084 | 2 |
| C89×#2986 | 2 |
| #8936 | 89 |