Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 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. C2×#22583632 | C2 | semidirect |
| 2. C22×#17985375 | C2 | semidirect |
| 3. #31826977 | C2 | semidirect |
| 4. #31826724 | C2 | semidirect |
| 5. #31826719 | C2 | semidirect |
| 6. #31826712 | C2 | semidirect |
| 7. #31826459 | C2 | semidirect |
| 8. #427×C283 | C2 | semidirect |
| 12. C2×Dic1132 | C22 | semidirect |
| 13. C2×#17985381 | C22 | semidirect |
| 14. C2×D2264 | C22 | semidirect |
| 24. #22583533 | C22 | semidirect |
| 25. #22583530 | C22 | semidirect |
| 28. #107×C283 | C22 | semidirect |
| 29. #106×C283 | C22 | semidirect |
| 54. C2×C8×C283 | D4 | semidirect |
| 105. C283 | #3054 | semidirect |
| 113. #427 | D283 | semidirect |
| 132. #107 | C2×D283 | semidirect |
| 133. #106 | C2×D283 | semidirect |
| 157. C2×C8 | D1132 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583632 | 2 |
| C22×#17985375 | 2 |
| #31826977 | 2 |
| #31826724 | 2 |
| #31826719 | 2 |
| #31826712 | 2 |
| #31826459 | 2 |
| #427×C283 | 2 |
| #3054 | 283 |