Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
466 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 137 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. #31827263 | C2 | semidirect |
| 2. C2×#22583636 | C2 | semidirect |
| 3. #31827231 | C2 | semidirect |
| 4. #31826732 | C2 | semidirect |
| 5. #31826725 | C2 | semidirect |
| 6. #31826514 | C2 | semidirect |
| 7. #31826449 | C2 | semidirect |
| 8. C2×#22583527 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C283 | C2 | semidirect |
| 11. #22583641 | C22 | semidirect |
| 15. #22583636 | C22 | semidirect |
| 21. #22583616 | C22 | semidirect |
| 26. #22583546 | C22 | semidirect |
| 27. #22583529 | C22 | semidirect |
| 28. #22583527 | C22 | semidirect |
| 29. #22583527 | C22 | semidirect |
| 34. C2×SD16×C283 | C22 | semidirect |
| 35. C2×D8×C283 | C22 | semidirect |
| 147. C283 | #3068 | semidirect |
| 151. C2×AGL(1,ℤ/8) | D283 | semidirect |
| 171. C2×SD16 | C2×D283 | semidirect |
| 173. C2×D8 | C2×D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827263 | 2 |
| C2×#22583636 | 2 |
| #31827231 | 2 |
| #31826732 | 2 |
| #31826725 | 2 |
| #31826514 | 2 |
| #31826449 | 2 |
| C2×#22583527 | 2 |
| C2×AGL(1,ℤ/8)×C283 | 2 |
| #3068 | 283 |