Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
526 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 526 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×#22583635 | C2 | semidirect |
| 2. C22×#17985377 | C2 | semidirect |
| 3. #31826939 | C2 | semidirect |
| 4. #31826677 | C2 | semidirect |
| 5. #31826657 | C2 | semidirect |
| 6. #31826492 | C2 | semidirect |
| 7. #31826470 | C2 | semidirect |
| 8. #31826461 | C2 | semidirect |
| 9. #535×C283 | C2 | semidirect |
| 12. C2×#17985379 | C22 | semidirect |
| 15. C2×#17985377 | C22 | semidirect |
| 18. C4×D1132 | C22 | semidirect |
| 22. C4⋊(C283⋊C8) | C22 | semidirect |
| 23. #22583534 | C22 | semidirect |
| 24. #22583531 | C22 | semidirect |
| 25. #22583531 | C22 | semidirect |
| 28. #127×C283 | C22 | semidirect |
| 29. #124×C283 | C22 | semidirect |
| 36. C2×D1132 | D4 | semidirect |
| 121. C283 | #3041 | semidirect |
| 125. #535 | D283 | semidirect |
| 142. #127 | C2×D283 | semidirect |
| 143. #124 | 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 |
| C22×#17985377 | 2 |
| #31826939 | 2 |
| #31826677 | 2 |
| #31826657 | 2 |
| #31826492 | 2 |
| #31826470 | 2 |
| #31826461 | 2 |
| #535×C283 | 2 |
| #3041 | 283 |