Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
408 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 408 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 |
|---|---|---|
| 1. #31827181 | C2 | semidirect |
| 2. #31827137 | C2 | semidirect |
| 3. #31826813 | C2 | semidirect |
| 4. #31826792 | C2 | semidirect |
| 5. #31826702 | C2 | semidirect |
| 6. #31826661 | C2 | semidirect |
| 7. #31826613 | C2 | semidirect |
| 8. C4×#17985379 | C2 | semidirect |
| 9. #31826530 | C2 | semidirect |
| 10. #31826460 | C2 | semidirect |
| 11. #477×C283 | C2 | semidirect |
| 132. C283 | #3305 | semidirect |
| 138. #477 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827181 | 2 |
| #31827137 | 2 |
| #31826813 | 2 |
| #31826792 | 2 |
| #31826702 | 2 |
| #31826661 | 2 |
| #31826613 | 2 |
| C4×#17985379 | 2 |
| #31826530 | 2 |
| #31826460 | 2 |
| #477×C283 | 2 |
| #3305 | 283 |