Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
388 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 388 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. #31826799 | C2 | semidirect |
| 4. #31826757 | C2 | semidirect |
| 5. #31826705 | C2 | semidirect |
| 6. #31826672 | C2 | semidirect |
| 7. #31826622 | C2 | semidirect |
| 8. C4×Dic1132 | C2 | semidirect |
| 10. #103×D283 | C2 | semidirect |
| 11. #487×C283 | C2 | semidirect |
| 82. D1132 | Q16 | semidirect |
| 122. C283 | #3299 | semidirect |
| 126. #487 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827176 | 2 |
| #31827130 | 2 |
| #31826799 | 2 |
| #31826757 | 2 |
| #31826705 | 2 |
| #31826672 | 2 |
| #31826622 | 2 |
| C4×Dic1132 | 2 |
| C8×D1132 | 2 |
| #103×D283 | 2 |
| #487×C283 | 2 |
| #3299 | 283 |