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. #34036840 | C2 | semidirect |
| 3. #34036446 | C2 | semidirect |
| 4. #34036416 | C2 | semidirect |
| 5. #34036357 | C2 | semidirect |
| 6. #34036326 | C2 | semidirect |
| 7. #34036281 | C2 | semidirect |
| 8. C4×#17989791 | C2 | semidirect |
| 9. C8×D1172 | C2 | semidirect |
| 10. #102×D293 | C2 | semidirect |
| 11. #486×C293 | C2 | semidirect |
| 15. C2×#17989790 | C22 | semidirect |
| 16. C2×C8×D293 | C22 | semidirect |
| 18. #22627604 | C22 | semidirect |
| 23. C4×Dic586 | C22 | semidirect |
| 27. C4⋊C4×D293 | C22 | semidirect |
| 28. #22627556 | C22 | semidirect |
| 29. #22627555 | C22 | semidirect |
| 30. C4⋊#14556873 | C22 | semidirect |
| 31. #22627549 | C22 | semidirect |
| 33. #22627545 | C22 | semidirect |
| 35. #22627536 | C22 | semidirect |
| 36. C4⋊Q8×C293 | C22 | semidirect |
| 38. #102×C293 | C22 | semidirect |
| 39. #102×C293 | C22 | semidirect |
| 40. C4×C8×C293 | C22 | semidirect |
| 85. D1172 | SD16 | semidirect |
| 136. C293 | #3295 | semidirect |
| 140. #486 | D293 | semidirect |
| 154. C4⋊Q8 | C2×D293 | semidirect |
| 174. #102 | C2×D293 | semidirect |
| 175. #102 | C2×D293 | semidirect |
| 177. C4×C8 | C2×D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #34036840 | 2 |
| #34036764 | 2 |
| #34036446 | 2 |
| #34036416 | 2 |
| #34036357 | 2 |
| #34036326 | 2 |
| #34036281 | 2 |
| C4×#17989791 | 2 |
| C8×D1172 | 2 |
| #102×D293 | 2 |
| #486×C293 | 2 |
| #3295 | 293 |