Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
408 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 115 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. #31827013 | C2 | semidirect |
| 2. #31827000 | C2 | semidirect |
| 3. #31826875 | C2 | semidirect |
| 4. #31826852 | C2 | semidirect |
| 5. #31826825 | C2 | semidirect |
| 6. #31826717 | C2 | semidirect |
| 7. #31826710 | C2 | semidirect |
| 8. #31826556 | C2 | semidirect |
| 9. #31826545 | C2 | semidirect |
| 10. #31826417 | C2 | semidirect |
| 11. #490×C283 | C2 | semidirect |
| 99. C283⋊C8 | #41 | semidirect |
| 137. C283 | #3171 | semidirect |
| 143. #490 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827013 | 2 |
| #31827000 | 2 |
| #31826875 | 2 |
| #31826852 | 2 |
| #31826825 | 2 |
| #31826717 | 2 |
| #31826710 | 2 |
| #31826556 | 2 |
| #31826545 | 2 |
| #31826417 | 2 |
| #490×C283 | 2 |
| #3171 | 283 |