Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
792 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 229 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×C8×D283 | C2 | semidirect |
| 3. C2×#22583568 | C2 | semidirect |
| 4. #31826460 | C2 | direct (N × H) |
| 5. C2×#22583534 | C2 | semidirect |
| 6. C2×#22583532 | C2 | semidirect |
| 7. C2×#22583530 | C2 | semidirect |
| 8. C2×#103×C283 | C2 | semidirect |
| 11. C2×#17985393 | C4 | semidirect |
| 19. C2×C8×D283 | C22 | semidirect |
| 21. #22583568 | C22 | semidirect |
| 25. #22583534 | C22 | semidirect |
| 26. #22583532 | C22 | semidirect |
| 27. #22583530 | C22 | semidirect |
| 31. #103×C283 | C22 | semidirect |
| 36. #17985393 | C2×C4 | semidirect |
| 122. C2×C283 | #416 | semidirect |
| 128. C283 | C2×#416 | semidirect |
| 135. C2×#103 | D283 | semidirect |
| 158. #103 | C2×D283 | semidirect |
| 253. C2 | #31826460 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#17985393 | 2 |
| C22×C8×D283 | 2 |
| C2×#22583568 | 2 |
| #31826460 | 2 |
| C2×#22583534 | 2 |
| C2×#22583532 | 2 |
| C2×#22583530 | 2 |
| C2×#103×C283 | 2 |
| C2×#416 | 283 |