Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
370 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 113 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. #31827266 | C2 | semidirect |
| 2. #31826901 | C2 | semidirect |
| 3. #31826899 | C2 | semidirect |
| 4. #31826897 | C2 | semidirect |
| 5. #31826894 | C2 | semidirect |
| 6. D16×D283 | C2 | semidirect |
| 7. #31826881 | C2 | semidirect |
| 8. C2×D16×C283 | C2 | semidirect |
| 12. #22583632 | C22 | semidirect |
| 13. #22583629 | C22 | semidirect |
| 14. D8×D283 | C22 | semidirect |
| 16. Dic2264 | C22 | semidirect |
| 17. #22583555 | C22 | semidirect |
| 18. #22583554 | C22 | semidirect |
| 19. D4528 | C22 | semidirect |
| 20. #22583551 | C22 | semidirect |
| 21. #22583550 | C22 | semidirect |
| 22. #22583549 | C22 | semidirect |
| 23. C16×D283 | C22 | semidirect |
| 24. C2×D8×C283 | C22 | semidirect |
| 25. D16×C283 | C22 | semidirect |
| 26. D16×C283 | C22 | semidirect |
| 27. C2×C16×C283 | C22 | semidirect |
| 84. C283 | #3415 | semidirect |
| 92. C2×D16 | D283 | semidirect |
| 100. C2×D8 | C2×D283 | semidirect |
| 107. D16 | C2×D283 | semidirect |
| 108. D16 | C2×D283 | semidirect |
| 112. C2×C16 | C2×D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827266 | 2 |
| #31826901 | 2 |
| #31826899 | 2 |
| #31826897 | 2 |
| #31826894 | 2 |
| D16×D283 | 2 |
| #31826881 | 2 |
| C2×D16×C283 | 2 |
| #3415 | 283 |