Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
392 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 117 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. #125×D283 | C2 | semidirect |
| 3. #31826835 | C2 | semidirect |
| 4. #31826834 | C2 | semidirect |
| 5. #31826829 | C2 | semidirect |
| 6. #31826818 | C2 | semidirect |
| 7. #31826463 | C2 | semidirect |
| 8. #31826417 | C2 | semidirect |
| 9. #490×C283 | C2 | semidirect |
| 90. C283 | #3142 | semidirect |
| 97. #490 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827013 | 2 |
| #125×D283 | 2 |
| #31826835 | 2 |
| #31826834 | 2 |
| #31826829 | 2 |
| #31826818 | 2 |
| #31826463 | 2 |
| #31826417 | 2 |
| #490×C283 | 2 |
| #3142 | 283 |