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. C2×#22583635 | C2 | semidirect |
| 2. C2×#22583635 | C2 | semidirect |
| 3. #31827232 | C2 | semidirect |
| 4. #31826733 | C2 | semidirect |
| 5. #31826730 | C2 | semidirect |
| 6. #31826513 | C2 | semidirect |
| 7. #31826449 | C2 | semidirect |
| 8. C2×#22583526 | C2 | semidirect |
| 9. #575×C283 | C2 | semidirect |
| 16. C2×#17985379 | C22 | semidirect |
| 18. C2×#17985377 | C22 | semidirect |
| 20. #22583617 | C22 | semidirect |
| 25. #22583545 | C22 | semidirect |
| 26. #22583529 | C22 | semidirect |
| 27. #22583527 | C22 | semidirect |
| 28. #22583526 | C22 | semidirect |
| 32. #137×C283 | C22 | semidirect |
| 34. AGL(1,ℤ/8)×C283 | C22 | semidirect |
| 147. C283 | #3068 | semidirect |
| 149. #575 | D283 | semidirect |
| 162. #137 | C2×D283 | semidirect |
| 168. AGL(1,ℤ/8) | C2×D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583635 | 2 |
| #31827232 | 2 |
| #31826733 | 2 |
| #31826730 | 2 |
| #31826513 | 2 |
| #31826449 | 2 |
| C2×#22583526 | 2 |
| #575×C283 | 2 |
| #3068 | 283 |