Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
456 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 175 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. #31826573 | C2 | semidirect |
| 4. #31826572 | C2 | semidirect |
| 5. #31826571 | C2 | semidirect |
| 6. C4×#17985382 | C2 | semidirect |
| 7. #31826557 | C2 | semidirect |
| 11. #441×C283 | C2 | semidirect |
| 15. Q16×D283 | C4 | semidirect |
| 108. C283 | #2950 | semidirect |
| 115. #441 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D283 | 2 |
| #31826941 | 2 |
| #31826573 | 2 |
| #31826572 | 2 |
| #31826571 | 2 |
| C4×#17985382 | 2 |
| #31826557 | 2 |
| #31826500 | 2 |
| #31826472 | 2 |
| #31826422 | 2 |
| #441×C283 | 2 |
| #2950 | 283 |