Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
548 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 131 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×#22583634 | C2 | semidirect |
| 2. #31827013 | C2 | semidirect |
| 3. C4×D4×D283 | C2 | semidirect |
| 4. #31826679 | C2 | semidirect |
| 5. #31826678 | C2 | semidirect |
| 6. #31826671 | C2 | semidirect |
| 7. #31826670 | C2 | semidirect |
| 8. #31826657 | C2 | semidirect |
| 9. #31826487 | C2 | semidirect |
| 10. #31826463 | C2 | semidirect |
| 11. #459×C283 | C2 | semidirect |
| 20. #22583610 | C22 | semidirect |
| 21. #22583597 | C22 | semidirect |
| 34. C4⋊(C283⋊C8) | C22 | semidirect |
| 35. Dic283⋊C8 | C22 | semidirect |
| 36. #22583535 | C22 | semidirect |
| 37. #22583533 | C22 | semidirect |
| 38. #22583531 | C22 | semidirect |
| 40. #127×C283 | C22 | semidirect |
| 42. C4⋊C8×C283 | C22 | semidirect |
| 43. #102×C283 | C22 | semidirect |
| 52. D4×D283 | D4 | semidirect |
| 145. C4×C283 | AGL(1,ℤ/8) | semidirect |
| 160. C283 | #3036 | semidirect |
| 170. #459 | D283 | semidirect |
| 183. #127 | C2×D283 | semidirect |
| 200. C4⋊C8 | C2×D283 | semidirect |
| 204. #102 | C2×D283 | semidirect |
| 311. C4 | #22583634 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583634 | 2 |
| #31827013 | 2 |
| C4×D4×D283 | 2 |
| #31826679 | 2 |
| #31826678 | 2 |
| #31826671 | 2 |
| #31826670 | 2 |
| #31826657 | 2 |
| #31826487 | 2 |
| #31826463 | 2 |
| #459×C283 | 2 |
| #3036 | 283 |