Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
424 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 91 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. #26029239 | C2 | semidirect |
| 3. #26018798 | C2 | semidirect |
| 4. #26018668 | C2 | semidirect |
| 5. #26018116 | C2 | semidirect |
| 6. #26018114 | C2 | semidirect |
| 7. C89×#1521 | C2 | semidirect |
| 9. #19151993 | C4 | semidirect |
| 10. #19151988 | C4 | semidirect |
| 11. #19151968 | C4 | semidirect |
| 12. #19151964 | C4 | semidirect |
| 207. #1521 | D89 | semidirect |
| 212. C89 | #9370 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031285 | 2 |
| #26029239 | 2 |
| #26018798 | 2 |
| #26018668 | 2 |
| #26018116 | 2 |
| #26018114 | 2 |
| C89×#1521 | 2 |
| #9370 | 89 |