Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
806 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 806 conjugacy classes of subgroups — too many to draw. Only its 153 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. C22×#17985392 | C2 | semidirect |
| 2. C2×#22583636 | C2 | semidirect |
| 3. #31826608 | C2 | semidirect |
| 4. #31826603 | C2 | semidirect |
| 5. #31826598 | C2 | semidirect |
| 6. #31826464 | C2 | semidirect |
| 7. #31826429 | C2 | semidirect |
| 8. C2×#121×C283 | C2 | semidirect |
| 13. C2×#17985392 | C22 | semidirect |
| 14. C22×Dic566 | C22 | semidirect |
| 15. C22×D1132 | C22 | semidirect |
| 19. C2×#17985380 | C22 | semidirect |
| 20. C2×#17985377 | C22 | semidirect |
| 21. C2×#17985376 | C22 | semidirect |
| 22. #22583533 | C22 | semidirect |
| 23. #22583530 | C22 | semidirect |
| 24. C22⋊(C283⋊C8) | C22 | semidirect |
| 25. C22⋊(C283⋊C8) | C22 | semidirect |
| 27. C22×D4×C283 | C22 | semidirect |
| 32. #121×C283 | C22 | semidirect |
| 33. C2×C4⋊C4×C283 | C22 | semidirect |
| 41. #17985392 | D4 | semidirect |
| 85. Dic566 | C2×D4 | semidirect |
| 88. D1132 | C2×D4 | semidirect |
| 135. C22×C283 | AGL(1,ℤ/8) | semidirect |
| 155. C283 | #3006 | semidirect |
| 159. C2×#121 | D283 | semidirect |
| 174. C22×D4 | C2×D283 | semidirect |
| 184. #121 | C2×D283 | semidirect |
| 185. C2×C4⋊C4 | C2×D283 | semidirect |
| 295. C22 | #22583636 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#17985392 | 2 |
| C2×#22583636 | 2 |
| #31826608 | 2 |
| #31826603 | 2 |
| #31826598 | 2 |
| #31826464 | 2 |
| #31826429 | 2 |
| C2×#121×C283 | 2 |
| #3006 | 283 |