Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
408 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 1. #31826999 | C2 | semidirect |
| 2. #31826871 | C2 | semidirect |
| 3. #31826852 | C2 | semidirect |
| 4. #31826829 | C2 | semidirect |
| 5. #31826827 | C2 | semidirect |
| 6. #31826716 | C2 | semidirect |
| 7. #31826709 | C2 | semidirect |
| 8. C4×#17985380 | C2 | semidirect |
| 9. C4×#17985377 | C2 | semidirect |
| 10. C4×#17985376 | C2 | semidirect |
| 11. #532×C283 | C2 | semidirect |
| 91. C283⋊C8 | #41 | semidirect |
| 137. C283 | #3171 | semidirect |
| 139. #532 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31826999 | 2 |
| #31826871 | 2 |
| #31826852 | 2 |
| #31826829 | 2 |
| #31826827 | 2 |
| #31826716 | 2 |
| #31826709 | 2 |
| C4×#17985380 | 2 |
| C4×#17985377 | 2 |
| C4×#17985376 | 2 |
| #532×C283 | 2 |
| #3171 | 283 |