Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
526 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#22583635 | C2 | semidirect |
| 2. C22×D2264 | C2 | semidirect |
| 3. #31827029 | C2 | semidirect |
| 4. #31826939 | C2 | semidirect |
| 5. #31826683 | C2 | semidirect |
| 6. #31826659 | C2 | semidirect |
| 7. #31826491 | C2 | semidirect |
| 8. #31826469 | C2 | semidirect |
| 9. #416×C283 | C2 | semidirect |
| 13. C2×#17985379 | C22 | semidirect |
| 16. C2×#17985377 | C22 | semidirect |
| 18. #22583606 | C22 | semidirect |
| 19. #22583599 | C22 | semidirect |
| 23. #22583572 | C22 | semidirect |
| 26. Dic283⋊C8 | C22 | semidirect |
| 27. #22583530 | C22 | semidirect |
| 31. #103×C283 | C22 | semidirect |
| 32. #102×C283 | C22 | semidirect |
| 40. C2×D1132 | D4 | semidirect |
| 121. C283 | #3041 | semidirect |
| 131. #416 | D283 | semidirect |
| 152. #103 | C2×D283 | semidirect |
| 154. #102 | C2×D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583635 | 2 |
| C22×D2264 | 2 |
| #31827029 | 2 |
| #31826939 | 2 |
| #31826683 | 2 |
| #31826659 | 2 |
| #31826491 | 2 |
| #31826469 | 2 |
| #416×C283 | 2 |
| #3041 | 283 |