Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
448 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 448 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. #31827017 | C2 | semidirect |
| 3. #31826796 | C2 | semidirect |
| 4. #31826793 | C2 | semidirect |
| 5. #31826753 | C2 | semidirect |
| 6. #31826668 | C2 | semidirect |
| 8. #31826556 | C2 | semidirect |
| 9. SD16×Dic283 | C2 | semidirect |
| 10. #31826515 | C2 | semidirect |
| 14. #22583609 | C22 | semidirect |
| 15. #22583608 | C22 | semidirect |
| 19. Q8×Dic283 | C22 | semidirect |
| 21. #22583575 | C22 | semidirect |
| 30. #22583542 | C22 | semidirect |
| 31. #22583541 | C22 | semidirect |
| 32. Dic283⋊C8 | C22 | semidirect |
| 33. #22583535 | C22 | semidirect |
| 34. #22583534 | C22 | semidirect |
| 37. C8×Dic283 | C22 | semidirect |
| 91. C2×Dic283 | SD16 | semidirect |
| 136. C283 | #3101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827017 | 2 |
| C2×D4×Dic283 | 2 |
| #31826796 | 2 |
| #31826793 | 2 |
| #31826753 | 2 |
| #31826668 | 2 |
| #31826616 | 2 |
| #31826556 | 2 |
| SD16×Dic283 | 2 |
| #31826515 | 2 |
| #450×C283 | 2 |
| #3101 | 283 |