Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
450 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 121 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. #34036660 | C2 | semidirect |
| 2. C2×D4×Dic293 | C2 | semidirect |
| 3. #34036460 | C2 | semidirect |
| 4. #34036440 | C2 | semidirect |
| 5. #34036431 | C2 | semidirect |
| 6. #34036342 | C2 | semidirect |
| 7. #34036280 | C2 | semidirect |
| 8. #34036241 | C2 | semidirect |
| 9. #34036226 | C2 | semidirect |
| 10. #34036183 | C2 | semidirect |
| 15. #22627615 | C22 | semidirect |
| 16. #22627611 | C22 | semidirect |
| 19. #22627589 | C22 | semidirect |
| 25. D4×Dic293 | C22 | semidirect |
| 30. #22627557 | C22 | semidirect |
| 31. #22627556 | C22 | semidirect |
| 32. #22627553 | C22 | semidirect |
| 33. #22627549 | C22 | semidirect |
| 35. #22627545 | C22 | semidirect |
| 37. #22627534 | C22 | semidirect |
| 140. C293 | #3114 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #34036660 | 2 |
| C2×D4×Dic293 | 2 |
| #34036460 | 2 |
| #34036440 | 2 |
| #34036431 | 2 |
| #34036342 | 2 |
| #34036280 | 2 |
| #34036241 | 2 |
| #34036226 | 2 |
| #34036183 | 2 |
| #447×C293 | 2 |
| #3114 | 293 |