Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
398 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 398 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. #31827093 | C2 | semidirect |
| 3. #31826766 | C2 | semidirect |
| 4. #31826766 | C2 | semidirect |
| 5. #31826756 | C2 | semidirect |
| 6. #31826746 | C2 | semidirect |
| 7. #31826507 | C2 | semidirect |
| 8. #31826503 | C2 | semidirect |
| 11. #424×C283 | C2 | semidirect |
| 13. #22583610 | C22 | semidirect |
| 15. #22583602 | C22 | semidirect |
| 26. #22583544 | C22 | semidirect |
| 27. #22583544 | C22 | semidirect |
| 28. #22583544 | C22 | semidirect |
| 29. #22583542 | C22 | semidirect |
| 30. #22583542 | C22 | semidirect |
| 31. #22583542 | C22 | semidirect |
| 39. C4⋊C8×C283 | C22 | semidirect |
| 40. C4⋊C8×C283 | C22 | semidirect |
| 45. C2×D1132 | Q8 | semidirect |
| 124. C283 | #3081 | semidirect |
| 134. #424 | D283 | semidirect |
| 160. C4⋊C8 | C2×D283 | semidirect |
| 161. C4⋊C8 | C2×D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827093 | 2 |
| #31826939 | 2 |
| #31826766 | 2 |
| #31826756 | 2 |
| #31826746 | 2 |
| #31826507 | 2 |
| #31826503 | 2 |
| #31826471 | 2 |
| C2×#22583532 | 2 |
| #424×C283 | 2 |
| #3081 | 283 |