Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
524 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 141 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×#17985377 | C2 | semidirect |
| 2. C2×#22583617 | C2 | semidirect |
| 3. #31827029 | C2 | semidirect |
| 4. #31826716 | C2 | semidirect |
| 5. #31826699 | C2 | semidirect |
| 6. #31826501 | C2 | semidirect |
| 7. #31826470 | C2 | semidirect |
| 8. #31826469 | C2 | semidirect |
| 9. #535×C283 | C2 | semidirect |
| 16. C2×#17985376 | C22 | semidirect |
| 18. C22×C283⋊C8 | C22 | semidirect |
| 21. #22583584 | C22 | semidirect |
| 24. #22583543 | C22 | semidirect |
| 25. #22583541 | C22 | semidirect |
| 26. #22583531 | C22 | semidirect |
| 27. #22583530 | C22 | semidirect |
| 32. #121×C283 | C22 | semidirect |
| 46. C2×C283⋊C8 | D4 | semidirect |
| 125. C283 | #3058 | semidirect |
| 130. #535 | D283 | semidirect |
| 152. #121 | C2×D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#17985377 | 2 |
| C2×#22583617 | 2 |
| #31827029 | 2 |
| #31826716 | 2 |
| #31826699 | 2 |
| #31826501 | 2 |
| #31826470 | 2 |
| #31826469 | 2 |
| #535×C283 | 2 |
| #3058 | 283 |