Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 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 |
|---|---|---|
| 2. C2×C4×Dic566 | C2 | semidirect |
| 3. #31826801 | C2 | semidirect |
| 5. #31826773 | C2 | semidirect |
| 6. #31826688 | C2 | semidirect |
| 7. #31826623 | C2 | semidirect |
| 9. #31826573 | C2 | semidirect |
| 10. #31826567 | C2 | semidirect |
| 11. #432×C283 | C2 | semidirect |
| 131. C283 | #3117 | semidirect |
| 143. #432 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31826999 | 2 |
| C2×C4×Dic566 | 2 |
| #31826801 | 2 |
| #31826784 | 2 |
| #31826773 | 2 |
| #31826688 | 2 |
| #31826623 | 2 |
| #31826606 | 2 |
| #31826573 | 2 |
| #31826567 | 2 |
| #432×C283 | 2 |
| #3117 | 283 |