Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
462 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 125 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. #31827175 | C2 | semidirect |
| 3. #31826812 | C2 | semidirect |
| 4. #31826785 | C2 | semidirect |
| 5. #31826755 | C2 | semidirect |
| 6. #31826697 | C2 | semidirect |
| 7. #31826665 | C2 | semidirect |
| 8. #31826614 | C2 | semidirect |
| 9. C8×D1132 | C2 | semidirect |
| 10. #102×D283 | C2 | semidirect |
| 11. C4×SD16×C283 | C2 | semidirect |
| 14. C2×#17985379 | C22 | semidirect |
| 15. C2×C8×D283 | C22 | semidirect |
| 16. #22583610 | C22 | semidirect |
| 20. #22583586 | C22 | semidirect |
| 26. C4⋊C4×D283 | C22 | semidirect |
| 27. #22583541 | C22 | semidirect |
| 28. C4⋊(C283⋊C8) | C22 | semidirect |
| 29. #22583532 | C22 | semidirect |
| 30. #22583532 | C22 | semidirect |
| 32. #22583530 | C22 | semidirect |
| 33. (C2×D283)⋊C8 | C22 | semidirect |
| 35. C4×Q8×C283 | C22 | semidirect |
| 37. #106×C283 | C22 | semidirect |
| 38. #103×C283 | C22 | semidirect |
| 40. C4×C8×C283 | C22 | semidirect |
| 88. D1132 | SD16 | semidirect |
| 136. C283 | #3295 | semidirect |
| 146. C4×SD16 | D283 | semidirect |
| 162. C4×Q8 | C2×D283 | semidirect |
| 168. #106 | C2×D283 | semidirect |
| 170. #103 | C2×D283 | semidirect |
| 177. C4×C8 | C2×D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827175 | 2 |
| D4×D1132 | 2 |
| #31826812 | 2 |
| #31826785 | 2 |
| #31826755 | 2 |
| #31826697 | 2 |
| #31826665 | 2 |
| #31826614 | 2 |
| C8×D1132 | 2 |
| #102×D283 | 2 |
| C4×SD16×C283 | 2 |
| #3295 | 283 |