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. #31827016 | C2 | semidirect |
| 2. C4×D4×D283 | C2 | semidirect |
| 3. #31826780 | C2 | semidirect |
| 4. #31826742 | C2 | semidirect |
| 5. #31826661 | C2 | semidirect |
| 6. #31826660 | C2 | semidirect |
| 7. #31826600 | C2 | semidirect |
| 8. #31826547 | C2 | semidirect |
| 9. #31826545 | C2 | semidirect |
| 10. #31826517 | C2 | semidirect |
| 11. #474×C283 | C2 | semidirect |
| 17. #22583607 | C22 | semidirect |
| 25. #22583572 | C22 | semidirect |
| 31. #22583543 | C22 | semidirect |
| 32. C4⋊(C283⋊C8) | C22 | semidirect |
| 33. #22583532 | C22 | semidirect |
| 35. #22583530 | C22 | semidirect |
| 37. C8×Dic283 | C22 | semidirect |
| 38. C4⋊Q8×C283 | C22 | semidirect |
| 40. #107×C283 | C22 | semidirect |
| 41. C4⋊C8×C283 | C22 | semidirect |
| 96. D1132 | #41 | semidirect |
| 110. C4×D283 | D8 | semidirect |
| 115. D4×C283 | #41 | semidirect |
| 154. C283 | #3100 | semidirect |
| 160. #474 | D283 | semidirect |
| 172. C4⋊Q8 | C2×D283 | semidirect |
| 189. #107 | C2×D283 | semidirect |
| 191. C4⋊C8 | C2×D283 | semidirect |
| 256. D4 | #17985393 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827016 | 2 |
| C4×D4×D283 | 2 |
| #31826780 | 2 |
| #31826742 | 2 |
| #31826661 | 2 |
| #31826660 | 2 |
| #31826600 | 2 |
| #31826547 | 2 |
| #31826545 | 2 |
| #31826517 | 2 |
| #474×C283 | 2 |
| #3100 | 283 |