Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
472 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 2. #26020339 | C2 | semidirect |
| 3. #26020330 | C2 | semidirect |
| 5. #26018157 | C2 | semidirect |
| 6. #26018129 | C2 | semidirect |
| 9. #19151931 | C4 | semidirect |
| 11. #19151914 | C4 | semidirect |
| 224. C89 | #9522 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030172 | 2 |
| #26020339 | 2 |
| #26020330 | 2 |
| #26018795 | 2 |
| #26018157 | 2 |
| #26018129 | 2 |
| C89×#2976 | 2 |
| #9522 | 89 |