Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
404 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 125 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. #31827093 | C2 | semidirect |
| 3. #31826828 | C2 | semidirect |
| 4. #31826823 | C2 | semidirect |
| 5. #31826818 | C2 | semidirect |
| 6. #31826810 | C2 | semidirect |
| 7. #31826467 | C2 | semidirect |
| 8. #31826459 | C2 | semidirect |
| 9. C2×#22583531 | C2 | semidirect |
| 10. #31826423 | C2 | semidirect |
| 11. #418×C283 | C2 | semidirect |
| 15. #22583609 | C22 | semidirect |
| 18. #22583601 | C22 | semidirect |
| 26. #22583535 | C22 | semidirect |
| 27. #22583533 | C22 | semidirect |
| 28. #22583533 | C22 | semidirect |
| 29. #22583532 | C22 | semidirect |
| 32. #22583530 | C22 | semidirect |
| 33. #22583530 | C22 | semidirect |
| 34. #22583520 | C22 | semidirect |
| 35. C8×Dic283 | C22 | semidirect |
| 135. C283 | #3136 | semidirect |
| 143. #418 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827093 | 2 |
| #31827032 | 2 |
| #31826828 | 2 |
| #31826823 | 2 |
| #31826818 | 2 |
| #31826810 | 2 |
| #31826467 | 2 |
| #31826459 | 2 |
| C2×#22583531 | 2 |
| #31826423 | 2 |
| #418×C283 | 2 |
| #3136 | 283 |