Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
422 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 89 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. #26018763 | C2 | semidirect |
| 5. #26018726 | C2 | semidirect |
| 6. #26018114 | C2 | semidirect |
| 7. C89×#1274 | C2 | semidirect |
| 10. #19152003 | C4 | semidirect |
| 11. #19151996 | C4 | semidirect |
| 12. #19151945 | C4 | semidirect |
| 13. #19151945 | C4 | semidirect |
| 175. #1274 | D89 | semidirect |
| 176. C89 | #9279 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031390 | 2 |
| #26029327 | 2 |
| #26018763 | 2 |
| #26018759 | 2 |
| #26018726 | 2 |
| #26018114 | 2 |
| C89×#1274 | 2 |
| #9279 | 89 |