Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 149 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×#22583641 | C2 | semidirect |
| 2. C2×#22583636 | C2 | semidirect |
| 3. C2×#22583632 | C2 | semidirect |
| 4. #31827039 | C2 | semidirect |
| 5. #31827032 | C2 | semidirect |
| 6. #31826856 | C2 | semidirect |
| 7. #31826851 | C2 | semidirect |
| 8. #31826846 | C2 | semidirect |
| 9. #31826836 | C2 | semidirect |
| 10. #31826420 | C2 | semidirect |
| 11. C22×SD16×C283 | C2 | semidirect |
| 17. C2×Dic1132 | C22 | semidirect |
| 18. C2×#17985382 | C22 | semidirect |
| 19. C2×#17985381 | C22 | semidirect |
| 20. C2×#17985381 | C22 | semidirect |
| 22. C2×#17985379 | C22 | semidirect |
| 23. C2×D2264 | C22 | semidirect |
| 26. #22583608 | C22 | semidirect |
| 28. #22583599 | C22 | semidirect |
| 35. #22583520 | C22 | semidirect |
| 36. C8×Dic283 | C22 | semidirect |
| 64. #17985376 | D4 | semidirect |
| 85. C2×C8×C283 | D4 | semidirect |
| 148. C283 | #3154 | semidirect |
| 153. C22×SD16 | D283 | semidirect |
| 228. C2×C8 | C22⋊D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583641 | 2 |
| C2×#22583636 | 2 |
| C2×#22583632 | 2 |
| #31827039 | 2 |
| #31827032 | 2 |
| #31826856 | 2 |
| #31826851 | 2 |
| #31826846 | 2 |
| #31826836 | 2 |
| #31826420 | 2 |
| C22×SD16×C283 | 2 |
| #3154 | 283 |