Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
430 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 430 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. #26021199 | C2 | semidirect |
| 4. #26018970 | C2 | semidirect |
| 6. #26018107 | C2 | semidirect |
| 7. C89×#1290 | C2 | semidirect |
| 10. #19151992 | C4 | semidirect |
| 11. #19151967 | C4 | semidirect |
| 195. #1290 | D89 | semidirect |
| 197. C89 | #9376 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031281 | 2 |
| #26029388 | 2 |
| #26021199 | 2 |
| #26018970 | 2 |
| #26018778 | 2 |
| #26018107 | 2 |
| C89×#1290 | 2 |
| #9376 | 89 |