Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
492 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 127 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. #31827013 | C2 | semidirect |
| 2. C4×D4×D283 | C2 | semidirect |
| 3. #31826777 | C2 | semidirect |
| 4. #31826746 | C2 | semidirect |
| 5. #31826745 | C2 | semidirect |
| 6. #31826657 | C2 | semidirect |
| 7. #31826597 | C2 | semidirect |
| 8. D8×Dic283 | C2 | semidirect |
| 9. #31826545 | C2 | semidirect |
| 10. #31826517 | C2 | semidirect |
| 11. #459×C283 | C2 | semidirect |
| 16. #22583610 | C22 | semidirect |
| 23. D4×Dic283 | C22 | semidirect |
| 30. #22583544 | C22 | semidirect |
| 31. #22583543 | C22 | semidirect |
| 32. C4⋊(C283⋊C8) | C22 | semidirect |
| 35. #22583531 | C22 | semidirect |
| 37. C8×Dic283 | C22 | semidirect |
| 39. #127×C283 | C22 | semidirect |
| 41. C4⋊C8×C283 | C22 | semidirect |
| 42. #102×C283 | C22 | semidirect |
| 91. D1132 | #41 | semidirect |
| 107. C4×D283 | D8 | semidirect |
| 116. D4×C283 | #41 | semidirect |
| 154. C283 | #3100 | semidirect |
| 162. #459 | D283 | semidirect |
| 173. #127 | C2×D283 | semidirect |
| 191. C4⋊C8 | C2×D283 | semidirect |
| 195. #102 | C2×D283 | semidirect |
| 256. D4 | #17985391 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827013 | 2 |
| C4×D4×D283 | 2 |
| #31826777 | 2 |
| #31826746 | 2 |
| #31826745 | 2 |
| #31826657 | 2 |
| #31826597 | 2 |
| D8×Dic283 | 2 |
| #31826545 | 2 |
| #31826517 | 2 |
| #459×C283 | 2 |
| #3100 | 283 |