Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
406 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 406 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. #31827189 | C2 | semidirect |
| 2. #31827135 | C2 | semidirect |
| 3. #31826851 | C2 | semidirect |
| 4. #31826682 | C2 | semidirect |
| 5. #31826667 | C2 | semidirect |
| 6. #31826663 | C2 | semidirect |
| 7. #31826657 | C2 | semidirect |
| 8. #31826595 | C2 | semidirect |
| 9. #31826566 | C2 | semidirect |
| 10. C4×D2264 | C2 | semidirect |
| 11. #492×C283 | C2 | semidirect |
| 106. C8×C283 | #41 | semidirect |
| 132. C283 | #3397 | semidirect |
| 137. #492 | D283 | semidirect |
| 239. C8 | #17985391 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827189 | 2 |
| #31827135 | 2 |
| #31826851 | 2 |
| #31826682 | 2 |
| #31826667 | 2 |
| #31826663 | 2 |
| #31826657 | 2 |
| #31826595 | 2 |
| #31826566 | 2 |
| C4×D2264 | 2 |
| #492×C283 | 2 |
| #3397 | 283 |