Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
418 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 418 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. #31827201 | C2 | semidirect |
| 2. #31827135 | C2 | semidirect |
| 3. #31826853 | C2 | semidirect |
| 4. #31826678 | C2 | semidirect |
| 5. #31826662 | C2 | semidirect |
| 6. #31826658 | C2 | semidirect |
| 7. #31826657 | C2 | semidirect |
| 8. #31826595 | C2 | semidirect |
| 9. #31826577 | C2 | semidirect |
| 10. C4×#17985381 | C2 | semidirect |
| 11. #493×C283 | C2 | semidirect |
| 108. C8×C283 | #41 | semidirect |
| 134. C283 | #3399 | semidirect |
| 139. #493 | D283 | semidirect |
| 243. C8 | #17985391 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827201 | 2 |
| #31827135 | 2 |
| #31826853 | 2 |
| #31826678 | 2 |
| #31826662 | 2 |
| #31826658 | 2 |
| #31826657 | 2 |
| #31826595 | 2 |
| #31826577 | 2 |
| C4×#17985381 | 2 |
| #493×C283 | 2 |
| #3399 | 283 |