Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
494 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 494 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 |
|---|---|---|
| 2. C22×#17985379 | C2 | semidirect |
| 3. #31827039 | C2 | semidirect |
| 4. #31826939 | C2 | semidirect |
| 5. #31826683 | C2 | semidirect |
| 6. #31826669 | C2 | semidirect |
| 7. #31826493 | C2 | semidirect |
| 8. #31826459 | C2 | semidirect |
| 9. #419×C283 | C2 | semidirect |
| 18. #22583608 | C22 | semidirect |
| 19. #22583599 | C22 | semidirect |
| 26. Dic283⋊C8 | C22 | semidirect |
| 27. #22583533 | C22 | semidirect |
| 28. #22583530 | C22 | semidirect |
| 32. #103×C283 | C22 | semidirect |
| 116. C283 | #3042 | semidirect |
| 125. #419 | D283 | semidirect |
| 148. #103 | C2×D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583638 | 2 |
| C22×#17985379 | 2 |
| #31827039 | 2 |
| #31826939 | 2 |
| #31826683 | 2 |
| #31826669 | 2 |
| #31826493 | 2 |
| #31826459 | 2 |
| #419×C283 | 2 |
| #3042 | 283 |