Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 141 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. #34036783 | C2 | semidirect |
| 2. #34036475 | C2 | semidirect |
| 3. #34036440 | C2 | semidirect |
| 4. #34036409 | C2 | semidirect |
| 5. #34036363 | C2 | semidirect |
| 6. #34036321 | C2 | semidirect |
| 7. #34036263 | C2 | semidirect |
| 8. C4×#17989787 | C2 | semidirect |
| 9. D4×#14556873 | C2 | semidirect |
| 10. C2×#22627545 | C2 | semidirect |
| 11. D42×C293 | C2 | semidirect |
| 14. C2×#17989787 | C22 | semidirect |
| 15. C22×#14556873 | C22 | semidirect |
| 16. #22627624 | C22 | semidirect |
| 19. #22627598 | C22 | semidirect |
| 20. C4×D1172 | C22 | semidirect |
| 21. C2×C4⋊Dic293 | C22 | semidirect |
| 22. #22627557 | C22 | semidirect |
| 23. #22627557 | C22 | semidirect |
| 24. C4⋊#14556873 | C22 | semidirect |
| 27. #22627545 | C22 | semidirect |
| 28. #22627545 | C22 | semidirect |
| 29. #22627545 | C22 | semidirect |
| 30. #22627544 | C22 | semidirect |
| 31. C22⋊#14556873 | C22 | semidirect |
| 32. C4×#14556873 | C22 | semidirect |
| 103. D4×C293 | D8 | semidirect |
| 104. D4×C293 | #41 | semidirect |
| 142. C293 | #3294 | semidirect |
| 145. D42 | D293 | semidirect |
| 239. D4 | #17989787 | semidirect |
| 240. D4 | #17989801 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #34036783 | 2 |
| #34036475 | 2 |
| #34036440 | 2 |
| #34036409 | 2 |
| #34036363 | 2 |
| #34036321 | 2 |
| #34036263 | 2 |
| C4×#17989787 | 2 |
| D4×#14556873 | 2 |
| C2×#22627545 | 2 |
| D42×C293 | 2 |
| #3294 | 293 |