Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
326 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 326 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. M64×D89 | C2 | semidirect |
| 3. #368×D89 | C2 | semidirect |
| 4. #26018443 | C2 | semidirect |
| 5. #26018442 | C2 | semidirect |
| 6. #26018441 | C2 | semidirect |
| 7. C89×#1419 | C2 | semidirect |
| 17. #19151432 | C22 | semidirect |
| 20. #19151428 | C22 | semidirect |
| 23. M64×C89 | C22 | semidirect |
| 24. #368×C89 | C22 | semidirect |
| 125. D89 | #1419 | direct (N × H) |
| 132. #1419 | D89 | direct (N × H) |
| 133. C89 | C2×#1419 | semidirect |
| 146. M64 | C2×D89 | semidirect |
| 150. #368 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D16×D89 | 2 |
| M64×D89 | 2 |
| #368×D89 | 2 |
| #26018443 | 2 |
| #26018442 | 2 |
| #26018441 | 2 |
| C89×#1419 | 2 |
| C2×#1419 | 89 |