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 |
| 3. #34036494 | C2 | semidirect |
| 4. #34036489 | C2 | semidirect |
| 5. #34036484 | C2 | semidirect |
| 6. #34036476 | C2 | semidirect |
| 7. #34036135 | C2 | semidirect |
| 8. #34036131 | C2 | semidirect |
| 9. #34036126 | C2 | semidirect |
| 10. C2×#22627546 | C2 | semidirect |
| 11. #405×C293 | C2 | semidirect |
| 14. #22627624 | C22 | semidirect |
| 17. #22627616 | C22 | semidirect |
| 26. #22627549 | C22 | semidirect |
| 27. #22627549 | C22 | semidirect |
| 28. #22627549 | C22 | semidirect |
| 33. #22627546 | C22 | semidirect |
| 34. #22627546 | C22 | semidirect |
| 35. #22627546 | C22 | semidirect |
| 39. #97×C293 | C22 | semidirect |
| 40. C4×C8×C293 | C22 | semidirect |
| 135. C293 | #3136 | semidirect |
| 147. #405 | D293 | semidirect |
| 175. #97 | C2×D293 | semidirect |
| 176. C4×C8 | C2×D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #34036757 | 2 |
| #34036698 | 2 |
| #34036494 | 2 |
| #34036489 | 2 |
| #34036484 | 2 |
| #34036476 | 2 |
| #34036135 | 2 |
| #34036131 | 2 |
| #34036126 | 2 |
| C2×#22627546 | 2 |
| #405×C293 | 2 |
| #3136 | 293 |