Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
372 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 372 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. #26019858 | C2 | semidirect |
| 5. #26018288 | C2 | semidirect |
| 6. #26018226 | C2 | semidirect |
| 7. C89×#1335 | C2 | semidirect |
| 12. #19151978 | C22 | semidirect |
| 19. #19151419 | C22 | semidirect |
| 23. #364×C89 | C22 | semidirect |
| 24. C82×C89 | C22 | semidirect |
| 151. #1335 | D89 | semidirect |
| 152. C89 | #12312 | semidirect |
| 166. #364 | C2×D89 | semidirect |
| 169. C82 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26032052 | 2 |
| #26022334 | 2 |
| #26022333 | 2 |
| #26019858 | 2 |
| #26018288 | 2 |
| #26018226 | 2 |
| C89×#1335 | 2 |
| #12312 | 89 |