Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
354 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 354 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. #31827176 | C2 | semidirect |
| 3. #31826808 | C2 | semidirect |
| 4. #31826780 | C2 | semidirect |
| 5. #31826757 | C2 | semidirect |
| 6. #31826752 | C2 | semidirect |
| 7. #31826712 | C2 | semidirect |
| 8. C4×#17985381 | C2 | semidirect |
| 9. #31826544 | C2 | semidirect |
| 10. #31826506 | C2 | semidirect |
| 11. #500×C283 | C2 | semidirect |
| 121. C283 | #3357 | semidirect |
| 125. #500 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827181 | 2 |
| #31827176 | 2 |
| #31826808 | 2 |
| #31826780 | 2 |
| #31826757 | 2 |
| #31826752 | 2 |
| #31826712 | 2 |
| C4×#17985381 | 2 |
| #31826544 | 2 |
| #31826506 | 2 |
| #500×C283 | 2 |
| #3357 | 283 |