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×#22583637 | C2 | semidirect |
| 2. #31827016 | C2 | semidirect |
| 3. C4×D4×D283 | C2 | semidirect |
| 4. #31826683 | C2 | semidirect |
| 5. #31826682 | C2 | semidirect |
| 6. #31826667 | C2 | semidirect |
| 7. #31826661 | C2 | semidirect |
| 8. #31826660 | C2 | semidirect |
| 9. #31826487 | C2 | semidirect |
| 10. #31826465 | C2 | semidirect |
| 11. #461×C283 | C2 | semidirect |
| 20. #22583607 | C22 | semidirect |
| 21. #22583599 | C22 | semidirect |
| 34. C4⋊(C283⋊C8) | C22 | semidirect |
| 35. Dic283⋊C8 | C22 | semidirect |
| 36. #22583534 | C22 | semidirect |
| 37. #22583532 | C22 | semidirect |
| 38. #22583530 | C22 | semidirect |
| 40. C4⋊Q8×C283 | C22 | semidirect |
| 42. C4⋊C8×C283 | C22 | semidirect |
| 43. #103×C283 | C22 | semidirect |
| 54. D4×D283 | D4 | semidirect |
| 146. C4×C283 | AGL(1,ℤ/8) | semidirect |
| 160. C283 | #3036 | semidirect |
| 168. #461 | D283 | semidirect |
| 182. C4⋊Q8 | C2×D283 | semidirect |
| 200. C4⋊C8 | C2×D283 | semidirect |
| 202. #103 | C2×D283 | semidirect |
| 311. C4 | #22583637 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583637 | 2 |
| #31827016 | 2 |
| C4×D4×D283 | 2 |
| #31826683 | 2 |
| #31826682 | 2 |
| #31826667 | 2 |
| #31826661 | 2 |
| #31826660 | 2 |
| #31826487 | 2 |
| #31826465 | 2 |
| #461×C283 | 2 |
| #3036 | 283 |