Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
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. #34036757 | C2 | semidirect |
| 2. #34036493 | C2 | semidirect |
| 3. #34036488 | C2 | semidirect |
| 4. #34036483 | C2 | semidirect |
| 5. #34036475 | C2 | semidirect |
| 6. #34036134 | C2 | semidirect |
| 7. #34036130 | C2 | semidirect |
| 8. #34036125 | C2 | semidirect |
| 9. C2×#22627545 | C2 | semidirect |
| 10. #34036085 | C2 | semidirect |
| 14. #22627624 | C22 | semidirect |
| 16. #22627616 | C22 | semidirect |
| 21. #22627548 | C22 | semidirect |
| 22. #22627548 | C22 | semidirect |
| 23. #22627548 | C22 | semidirect |
| 28. #22627545 | C22 | semidirect |
| 29. #22627545 | C22 | semidirect |
| 30. #22627545 | C22 | semidirect |
| 31. #22627535 | C22 | semidirect |
| 32. C4×#14556873 | C22 | semidirect |
| 135. C293 | #3136 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #34036757 | 2 |
| #34036493 | 2 |
| #34036488 | 2 |
| #34036483 | 2 |
| #34036475 | 2 |
| #34036134 | 2 |
| #34036130 | 2 |
| #34036125 | 2 |
| C2×#22627545 | 2 |
| #34036085 | 2 |
| #535×C293 | 2 |
| #3136 | 293 |