Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
486 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 87 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. #26022054 | C2 | semidirect |
| 3. #26019014 | C2 | semidirect |
| 4. #26018299 | C2 | semidirect |
| 5. #26018298 | C2 | semidirect |
| 6. #26018297 | C2 | semidirect |
| 7. C89×#1361 | C2 | semidirect |
| 17. C4⋊#13083549 | C22 | semidirect |
| 20. #19151351 | C22 | semidirect |
| 23. C4⋊C16×C89 | C22 | semidirect |
| 24. #335×C89 | C22 | semidirect |
| 165. #1361 | D89 | semidirect |
| 166. C89 | #11964 | semidirect |
| 178. C4⋊C16 | C2×D89 | semidirect |
| 182. #335 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #493×D89 | 2 |
| #26022054 | 2 |
| #26019014 | 2 |
| #26018299 | 2 |
| #26018298 | 2 |
| #26018297 | 2 |
| C89×#1361 | 2 |
| #11964 | 89 |