Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
500 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 500 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×#22583632 | C2 | semidirect |
| 2. #31826976 | C2 | semidirect |
| 3. #31826723 | C2 | semidirect |
| 4. #31826718 | C2 | semidirect |
| 5. #31826711 | C2 | semidirect |
| 6. #31826503 | C2 | semidirect |
| 7. #31826462 | C2 | semidirect |
| 8. C22×M16×C283 | C2 | semidirect |
| 11. C2×Dic1132 | C22 | semidirect |
| 12. C2×#17985381 | C22 | semidirect |
| 13. C2×D2264 | C22 | semidirect |
| 20. #22583544 | C22 | semidirect |
| 21. #22583542 | C22 | semidirect |
| 22. #22583535 | C22 | semidirect |
| 23. #22583532 | C22 | semidirect |
| 56. C2×C8×C283 | D4 | semidirect |
| 105. C283 | #3054 | semidirect |
| 108. C22×M16 | D283 | semidirect |
| 156. 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×#22583632 | 2 |
| #31826976 | 2 |
| #31826723 | 2 |
| #31826718 | 2 |
| #31826711 | 2 |
| #31826503 | 2 |
| #31826462 | 2 |
| C22×M16×C283 | 2 |
| #3054 | 283 |