Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
392 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 99 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. #26019020 | C2 | semidirect |
| 4. #26018144 | C2 | semidirect |
| 13. #19151338 | C4 | semidirect |
| 14. #19151338 | C4 | semidirect |
| 15. #19151338 | C4 | semidirect |
| 143. C89 | #8918 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021085 | 2 |
| #26019020 | 2 |
| #26018844 | 2 |
| #26018144 | 2 |
| C89×#2980 | 2 |
| #8918 | 89 |