Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
644 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 644 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 3. #26020188 | C2 | semidirect |
| 4. #26020175 | C2 | semidirect |
| 6. #26018159 | C2 | semidirect |
| 7. C89×#1293 | C2 | semidirect |
| 12. #19151756 | C4 | semidirect |
| 14. #19151739 | C4 | semidirect |
| 257. #1293 | D89 | semidirect |
| 258. C89 | #9519 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029489 | 2 |
| #26029297 | 2 |
| #26020188 | 2 |
| #26020175 | 2 |
| #26018796 | 2 |
| #26018159 | 2 |
| C89×#1293 | 2 |
| #9519 | 89 |