Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
420 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 85 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. #26018889 | C2 | semidirect |
| 4. #26018802 | C2 | semidirect |
| 6. #26018124 | C2 | semidirect |
| 7. C89×#1288 | C2 | semidirect |
| 10. #19152003 | C4 | semidirect |
| 11. #19151971 | C4 | semidirect |
| 12. #19151949 | C4 | semidirect |
| 13. #19151945 | C4 | semidirect |
| 166. #1288 | D89 | semidirect |
| 167. C89 | #9415 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030970 | 2 |
| #26029322 | 2 |
| #26018889 | 2 |
| #26018802 | 2 |
| #26018798 | 2 |
| #26018124 | 2 |
| C89×#1288 | 2 |
| #9415 | 89 |