Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
504 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 99 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. #26029308 | C2 | semidirect |
| 3. C2×#19151331 | C2 | semidirect |
| 4. #26018613 | C2 | semidirect |
| 5. #26018139 | C2 | semidirect |
| 6. #26018095 | C2 | semidirect |
| 7. C89×#1504 | C2 | semidirect |
| 9. #19151931 | C4 | semidirect |
| 11. #19151914 | C4 | semidirect |
| 14. #19151748 | C4 | semidirect |
| 16. #19151731 | C4 | semidirect |
| 248. #1504 | D89 | semidirect |
| 253. C89 | #9264 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031013 | 2 |
| #26029308 | 2 |
| C2×#19151331 | 2 |
| #26018613 | 2 |
| #26018139 | 2 |
| #26018095 | 2 |
| C89×#1504 | 2 |
| #9264 | 89 |