Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
624 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 624 conjugacy classes of subgroups — too many to draw. Only its 91 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. #26029323 | C2 | semidirect |
| 3. #26020218 | C2 | semidirect |
| 4. #26018380 | C2 | semidirect |
| 5. C89×#2126 | C2 | semidirect |
| 8. #19151780 | C4 | semidirect |
| 10. #19151770 | C4 | semidirect |
| 197. #2126 | D89 | semidirect |
| 200. C89 | #13053 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029600 | 2 |
| #26029323 | 2 |
| #26020218 | 2 |
| #26018380 | 2 |
| C89×#2126 | 2 |
| #13053 | 89 |