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. #34036487 | C2 | semidirect |
| 5. #34036482 | C2 | semidirect |
| 6. #34036474 | C2 | semidirect |
| 7. #34036134 | C2 | semidirect |
| 8. #34036128 | C2 | semidirect |
| 9. #34036126 | C2 | semidirect |
| 10. #34036084 | C2 | semidirect |
| 11. C2×#102×C293 | C2 | semidirect |
| 15. #22627623 | C22 | semidirect |
| 18. #22627615 | C22 | semidirect |
| 26. #22627549 | C22 | semidirect |
| 27. #22627549 | C22 | semidirect |
| 28. #22627547 | C22 | semidirect |
| 29. #22627546 | C22 | semidirect |
| 30. #22627546 | C22 | semidirect |
| 33. #22627544 | C22 | semidirect |
| 34. #22627534 | C22 | semidirect |
| 35. C8×Dic293 | C22 | semidirect |
| 135. C293 | #3136 | semidirect |
| 146. C2×#102 | D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #34036760 | 2 |
| #34036696 | 2 |
| #34036492 | 2 |
| #34036487 | 2 |
| #34036482 | 2 |
| #34036474 | 2 |
| #34036134 | 2 |
| #34036128 | 2 |
| #34036126 | 2 |
| #34036084 | 2 |
| C2×#102×C293 | 2 |
| #3136 | 293 |