Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
462 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 123 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. #34036839 | C2 | semidirect |
| 3. #34036475 | C2 | semidirect |
| 4. #34036446 | C2 | semidirect |
| 5. #34036420 | C2 | semidirect |
| 6. #34036355 | C2 | semidirect |
| 7. #34036278 | C2 | semidirect |
| 8. C4×#17989789 | C2 | semidirect |
| 9. #34036194 | C2 | semidirect |
| 10. #102×D293 | C2 | semidirect |
| 11. #460×C293 | C2 | semidirect |
| 15. C2×C8×D293 | C22 | semidirect |
| 16. #22627624 | C22 | semidirect |
| 19. #22627600 | C22 | semidirect |
| 26. C4⋊C4×D293 | C22 | semidirect |
| 27. #22627556 | C22 | semidirect |
| 28. #22627555 | C22 | semidirect |
| 29. #22627548 | C22 | semidirect |
| 31. #22627545 | C22 | semidirect |
| 32. #22627545 | C22 | semidirect |
| 34. #22627536 | C22 | semidirect |
| 35. C4×#14556873 | C22 | semidirect |
| 36. C2×SD16×C293 | C22 | semidirect |
| 38. C4×Q8×C293 | C22 | semidirect |
| 39. C4⋊C8×C293 | C22 | semidirect |
| 40. #102×C293 | C22 | semidirect |
| 84. D1172 | SD16 | semidirect |
| 136. C293 | #3295 | semidirect |
| 144. #460 | D293 | semidirect |
| 152. C2×SD16 | C2×D293 | semidirect |
| 162. C4×Q8 | C2×D293 | semidirect |
| 169. C4⋊C8 | C2×D293 | semidirect |
| 175. #102 | C2×D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #34036839 | 2 |
| #34036764 | 2 |
| #34036475 | 2 |
| #34036446 | 2 |
| #34036420 | 2 |
| #34036355 | 2 |
| #34036278 | 2 |
| C4×#17989789 | 2 |
| #34036194 | 2 |
| #102×D293 | 2 |
| #460×C293 | 2 |
| #3295 | 293 |