Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
362 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 61 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. #26022334 | C2 | semidirect |
| 3. #26022333 | C2 | semidirect |
| 4. #26019923 | C2 | semidirect |
| 5. #26018292 | C2 | semidirect |
| 6. #26018229 | C2 | semidirect |
| 7. C89×#1336 | C2 | semidirect |
| 13. #19151978 | C22 | semidirect |
| 21. #19151419 | C22 | semidirect |
| 25. #364×C89 | C22 | semidirect |
| 26. #322×C89 | C22 | semidirect |
| 181. #1336 | D89 | semidirect |
| 182. C89 | #12315 | semidirect |
| 198. #364 | C2×D89 | semidirect |
| 201. #322 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26032046 | 2 |
| #26022334 | 2 |
| #26022333 | 2 |
| #26019923 | 2 |
| #26018292 | 2 |
| #26018229 | 2 |
| C89×#1336 | 2 |
| #12315 | 89 |