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. #31827015 | C2 | semidirect |
| 2. #31826875 | C2 | semidirect |
| 3. #31826855 | C2 | semidirect |
| 4. #31826831 | C2 | semidirect |
| 5. #31826824 | C2 | semidirect |
| 6. #31826716 | C2 | semidirect |
| 7. #31826713 | C2 | semidirect |
| 8. C4×#17985379 | C2 | semidirect |
| 9. C4×#17985377 | C2 | semidirect |
| 10. C4×#17985376 | C2 | semidirect |
| 11. #529×C283 | C2 | semidirect |
| 92. C283⋊C8 | #41 | semidirect |
| 137. C283 | #3171 | semidirect |
| 140. #529 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827015 | 2 |
| #31826875 | 2 |
| #31826855 | 2 |
| #31826831 | 2 |
| #31826824 | 2 |
| #31826716 | 2 |
| #31826713 | 2 |
| C4×#17985379 | 2 |
| C4×#17985377 | 2 |
| C4×#17985376 | 2 |
| #529×C283 | 2 |
| #3171 | 283 |