Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
294 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 81 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. C2×C32×D89 | C2 | semidirect |
| 3. #368×D89 | C2 | semidirect |
| 4. #26018437 | C2 | semidirect |
| 5. #26018436 | C2 | semidirect |
| 6. #26018435 | C2 | semidirect |
| 7. C89×#1417 | C2 | semidirect |
| 19. C2×#15667918 | C22 | semidirect |
| 22. #19151428 | C22 | semidirect |
| 25. C2×C32×C89 | C22 | semidirect |
| 26. #368×C89 | C22 | semidirect |
| 143. D89 | #1417 | direct (N × H) |
| 150. #1417 | D89 | direct (N × H) |
| 151. C89 | C2×#1417 | semidirect |
| 167. C2×C32 | C2×D89 | semidirect |
| 170. #368 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #508×D89 | 2 |
| C2×C32×D89 | 2 |
| #368×D89 | 2 |
| #26018437 | 2 |
| #26018436 | 2 |
| #26018435 | 2 |
| C89×#1417 | 2 |
| C2×#1417 | 89 |