Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
404 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 125 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. #34036760 | C2 | semidirect |
| 3. #34036492 | C2 | semidirect |
| 4. #34036490 | C2 | semidirect |
| 5. #34036485 | C2 | semidirect |
| 6. #34036474 | C2 | semidirect |
| 7. #34036135 | C2 | semidirect |
| 8. #34036125 | C2 | semidirect |
| 9. C2×#22627544 | C2 | semidirect |
| 10. #34036087 | C2 | semidirect |
| 11. #417×C293 | C2 | semidirect |
| 15. #22627623 | C22 | semidirect |
| 18. #22627615 | C22 | semidirect |
| 26. #22627548 | C22 | semidirect |
| 27. #22627548 | C22 | semidirect |
| 30. #22627545 | C22 | semidirect |
| 31. #22627545 | C22 | semidirect |
| 34. #22627534 | C22 | semidirect |
| 35. C8×Dic293 | C22 | semidirect |
| 39. #103×C293 | C22 | semidirect |
| 40. #102×C293 | C22 | semidirect |
| 135. C293 | #3136 | semidirect |
| 144. #417 | D293 | semidirect |
| 167. #103 | C2×D293 | semidirect |
| 174. #102 | C2×D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #34036760 | 2 |
| #34036693 | 2 |
| #34036492 | 2 |
| #34036490 | 2 |
| #34036485 | 2 |
| #34036474 | 2 |
| #34036135 | 2 |
| #34036125 | 2 |
| C2×#22627544 | 2 |
| #34036087 | 2 |
| #417×C293 | 2 |
| #3136 | 293 |