Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
| 2. #31826829 | C2 | semidirect |
| 3. #31826824 | C2 | semidirect |
| 4. #31826819 | C2 | semidirect |
| 5. #31826811 | C2 | semidirect |
| 6. #31826470 | C2 | semidirect |
| 7. #31826466 | C2 | semidirect |
| 8. #31826461 | C2 | semidirect |
| 9. C2×#22583531 | C2 | semidirect |
| 10. #31826421 | C2 | semidirect |
| 14. #22583610 | C22 | semidirect |
| 16. #22583602 | C22 | semidirect |
| 21. #22583534 | C22 | semidirect |
| 22. #22583534 | C22 | semidirect |
| 23. #22583534 | C22 | semidirect |
| 28. #22583531 | C22 | semidirect |
| 29. #22583531 | C22 | semidirect |
| 30. #22583531 | C22 | semidirect |
| 31. #22583521 | C22 | semidirect |
| 32. C4×C283⋊C8 | C22 | semidirect |
| 135. C283 | #3136 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827093 | 2 |
| #31826829 | 2 |
| #31826824 | 2 |
| #31826819 | 2 |
| #31826811 | 2 |
| #31826470 | 2 |
| #31826466 | 2 |
| #31826461 | 2 |
| C2×#22583531 | 2 |
| #31826421 | 2 |
| #535×C283 | 2 |
| #3136 | 283 |