Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
452 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 123 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. #31827264 | C2 | semidirect |
| 2. C2×#22583633 | C2 | semidirect |
| 3. #131×D283 | C2 | semidirect |
| 4. #31826737 | C2 | semidirect |
| 5. #31826736 | C2 | semidirect |
| 6. #31826735 | C2 | semidirect |
| 7. #31826731 | C2 | semidirect |
| 8. #31826730 | C2 | semidirect |
| 9. #108×D283 | C2 | semidirect |
| 10. #31826448 | C2 | semidirect |
| 11. #473×C283 | C2 | semidirect |
| 25. C2×#17985379 | C22 | semidirect |
| 26. C2×D2264 | C22 | semidirect |
| 37. #22583546 | C22 | semidirect |
| 38. #22583545 | C22 | semidirect |
| 39. #22583529 | C22 | semidirect |
| 40. #22583526 | C22 | semidirect |
| 41. #22583526 | C22 | semidirect |
| 43. C2×Q16×C283 | C22 | semidirect |
| 45. #108×C283 | C22 | semidirect |
| 46. #101×C283 | C22 | semidirect |
| 166. C283 | #3067 | semidirect |
| 172. #473 | D283 | semidirect |
| 193. C2×Q16 | C2×D283 | semidirect |
| 209. #108 | C2×D283 | semidirect |
| 211. #101 | C2×D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827264 | 2 |
| C2×#22583633 | 2 |
| #131×D283 | 2 |
| #31826737 | 2 |
| #31826736 | 2 |
| #31826735 | 2 |
| #31826731 | 2 |
| #31826730 | 2 |
| #108×D283 | 2 |
| #31826448 | 2 |
| #473×C283 | 2 |
| #3067 | 283 |