Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
450 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 121 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. #31826996 | C2 | semidirect |
| 2. C2×D4×Dic283 | C2 | semidirect |
| 3. #31826796 | C2 | semidirect |
| 4. #31826776 | C2 | semidirect |
| 5. #31826767 | C2 | semidirect |
| 6. #31826678 | C2 | semidirect |
| 7. #31826616 | C2 | semidirect |
| 8. #31826577 | C2 | semidirect |
| 9. #31826562 | C2 | semidirect |
| 10. #31826519 | C2 | semidirect |
| 15. #22583601 | C22 | semidirect |
| 16. #22583597 | C22 | semidirect |
| 19. #22583575 | C22 | semidirect |
| 25. D4×Dic283 | C22 | semidirect |
| 30. #22583543 | C22 | semidirect |
| 31. #22583542 | C22 | semidirect |
| 32. Dic283⋊C8 | C22 | semidirect |
| 33. #22583535 | C22 | semidirect |
| 35. #22583531 | C22 | semidirect |
| 37. #22583520 | C22 | semidirect |
| 140. C283 | #3114 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31826996 | 2 |
| C2×D4×Dic283 | 2 |
| #31826796 | 2 |
| #31826776 | 2 |
| #31826767 | 2 |
| #31826678 | 2 |
| #31826616 | 2 |
| #31826577 | 2 |
| #31826562 | 2 |
| #31826519 | 2 |
| #447×C283 | 2 |
| #3114 | 283 |