Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
466 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 129 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. #31827265 | C2 | semidirect |
| 2. C2×#22583636 | C2 | semidirect |
| 3. C2×#22583636 | C2 | semidirect |
| 4. #31827231 | C2 | semidirect |
| 5. #31826734 | C2 | semidirect |
| 6. #31826727 | C2 | semidirect |
| 7. #31826513 | C2 | semidirect |
| 8. #31826447 | C2 | semidirect |
| 9. C2×#100×C283 | C2 | semidirect |
| 13. #22583643 | C22 | semidirect |
| 15. #22583638 | C22 | semidirect |
| 22. C2×#17985380 | C22 | semidirect |
| 24. C2×#17985377 | C22 | semidirect |
| 25. #22583618 | C22 | semidirect |
| 30. #22583545 | C22 | semidirect |
| 31. #22583528 | C22 | semidirect |
| 32. #22583526 | C22 | semidirect |
| 36. #100×C283 | C22 | semidirect |
| 147. C283 | #3068 | semidirect |
| 157. C2×#100 | D283 | semidirect |
| 184. #100 | C2×D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827265 | 2 |
| C2×#22583636 | 2 |
| #31827231 | 2 |
| #31826734 | 2 |
| #31826727 | 2 |
| #31826513 | 2 |
| #31826447 | 2 |
| C2×#100×C283 | 2 |
| #3068 | 283 |