Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
760 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 165 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. C22×Dic1132 | C2 | semidirect |
| 3. C22×#17985380 | C2 | semidirect |
| 4. C2×#22583590 | C2 | semidirect |
| 5. #31826628 | C2 | direct (N × H) |
| 6. C2×#22583533 | C2 | semidirect |
| 7. C2×(C2×D283)⋊C8 | C2 | semidirect |
| 8. C2×#102×C283 | C2 | semidirect |
| 19. C2×Dic1132 | C22 | semidirect |
| 21. C2×#17985380 | C22 | semidirect |
| 24. #22583590 | C22 | semidirect |
| 27. #22583533 | C22 | semidirect |
| 28. (C2×D283)⋊C8 | C22 | semidirect |
| 32. #102×C283 | C22 | semidirect |
| 130. C2×C283 | #452 | semidirect |
| 135. C283 | C2×#452 | semidirect |
| 143. C2×#102 | D283 | semidirect |
| 167. #102 | C2×D283 | semidirect |
| 267. C2 | #31826628 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#17985391 | 2 |
| C22×Dic1132 | 2 |
| C22×#17985380 | 2 |
| C2×#22583590 | 2 |
| #31826628 | 2 |
| C2×#22583533 | 2 |
| C2×(C2×D283)⋊C8 | 2 |
| C2×#102×C283 | 2 |
| C2×#452 | 283 |