Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
462 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 131 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×Q32×D89 | C2 | semidirect |
| 3. #26022568 | C2 | direct (N × H) |
| 4. C2×Dic1424 | C2 | semidirect |
| 5. C2×#19151438 | C2 | semidirect |
| 6. C2×#19151436 | C2 | semidirect |
| 7. C2×#19151431 | C2 | semidirect |
| 8. C2×SD64×C89 | C2 | semidirect |
| 17. Q32×D89 | C22 | semidirect |
| 20. Dic1424 | C22 | semidirect |
| 21. #19151438 | C22 | semidirect |
| 22. #19151436 | C22 | semidirect |
| 23. #19151431 | C22 | semidirect |
| 27. SD64×C89 | C22 | semidirect |
| 125. C2×C89 | #2264 | semidirect |
| 134. C2×SD64 | D89 | semidirect |
| 136. C89 | C2×#2264 | semidirect |
| 153. SD64 | C2×D89 | semidirect |
| 253. C2 | #26022568 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152027 | 2 |
| C2×Q32×D89 | 2 |
| #26022568 | 2 |
| C2×Dic1424 | 2 |
| C2×#19151438 | 2 |
| C2×#19151436 | 2 |
| C2×#19151431 | 2 |
| C2×SD64×C89 | 2 |
| C2×#2264 | 89 |