Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 115 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. #31827193 | C2 | semidirect |
| 3. #31826856 | C2 | semidirect |
| 5. #31826686 | C2 | semidirect |
| 6. #31826676 | C2 | semidirect |
| 7. #31826668 | C2 | semidirect |
| 8. #31826592 | C2 | semidirect |
| 9. #31826562 | C2 | semidirect |
| 10. C4×#17985382 | C2 | semidirect |
| 121. C283 | #3400 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827201 | 2 |
| #31827193 | 2 |
| #31826856 | 2 |
| #31826837 | 2 |
| #31826686 | 2 |
| #31826676 | 2 |
| #31826668 | 2 |
| #31826592 | 2 |
| #31826562 | 2 |
| C4×#17985382 | 2 |
| #460×C283 | 2 |
| #3400 | 283 |