Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
350 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 3. #31826844 | C2 | semidirect |
| 5. #31826675 | C2 | semidirect |
| 6. #31826672 | C2 | semidirect |
| 8. #31826596 | C2 | semidirect |
| 9. #31826570 | C2 | semidirect |
| 11. #557×C283 | C2 | semidirect |
| 119. C283 | #3398 | semidirect |
| 121. #557 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827188 | 2 |
| #31826857 | 2 |
| #31826844 | 2 |
| #31826687 | 2 |
| #31826675 | 2 |
| #31826672 | 2 |
| #31826667 | 2 |
| #31826596 | 2 |
| #31826570 | 2 |
| C4×#17985379 | 2 |
| #557×C283 | 2 |
| #3398 | 283 |