Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
492 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 189 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 |
|---|---|---|
| 2. #31826942 | C2 | semidirect |
| 4. #31826567 | C2 | semidirect |
| 5. C4×#17985381 | C2 | semidirect |
| 6. #31826503 | C2 | semidirect |
| 7. #31826475 | C2 | semidirect |
| 9. #405×C283 | C2 | semidirect |
| 12. C2×#17985381 | C4 | semidirect |
| 15. C4×Dic566 | C22 | semidirect |
| 23. #22583544 | C22 | semidirect |
| 24. #22583542 | C22 | semidirect |
| 25. #22583535 | C22 | semidirect |
| 30. #97×C283 | C22 | semidirect |
| 31. C4×C8×C283 | C22 | semidirect |
| 35. C2×Dic566 | C2×C4 | semidirect |
| 43. #17985381 | C2×C4 | semidirect |
| 44. #17985381 | C2×C4 | semidirect |
| 56. C2×C8×C283 | C2×C4 | semidirect |
| 103. C283 | #2949 | semidirect |
| 113. #405 | D283 | semidirect |
| 134. #97 | C2×D283 | semidirect |
| 135. C4×C8 | C2×D283 | semidirect |
| 151. C2×C8 | C4×D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#17985381 | 2 |
| #31826942 | 2 |
| #31826939 | 2 |
| #31826567 | 2 |
| C4×#17985381 | 2 |
| #31826503 | 2 |
| #31826475 | 2 |
| #31826471 | 2 |
| #405×C283 | 2 |
| #2949 | 283 |