Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
412 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 87 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. #26022064 | C2 | semidirect |
| 2. #26018293 | C2 | semidirect |
| 3. #26018289 | C2 | semidirect |
| 5. #19151419 | C22 | semidirect |
| 122. C89 | #11992 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022064 | 2 |
| #26018293 | 2 |
| #26018289 | 2 |
| C89×#3151 | 2 |
| #11992 | 89 |