Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
622 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 622 conjugacy classes of subgroups — too many to draw. Only its 113 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. #26022869 | C2 | semidirect |
| 5. C2×#19151323 | C2 | semidirect |
| 6. #26018119 | C2 | semidirect |
| 7. C89×#1289 | C2 | semidirect |
| 13. #19151530 | C4 | semidirect |
| 15. #19151516 | C4 | semidirect |
| 235. #1289 | D89 | semidirect |
| 236. C89 | #9204 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26025997 | 2 |
| #26022869 | 2 |
| #26018821 | 2 |
| #26018819 | 2 |
| C2×#19151323 | 2 |
| #26018119 | 2 |
| C89×#1289 | 2 |
| #9204 | 89 |