Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
494 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 494 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. #34036782 | C2 | semidirect |
| 2. #34036764 | C2 | semidirect |
| 3. #34036441 | C2 | semidirect |
| 4. #34036406 | C2 | semidirect |
| 5. #34036364 | C2 | semidirect |
| 6. #34036321 | C2 | semidirect |
| 7. #34036264 | C2 | semidirect |
| 8. C4×D2344 | C2 | semidirect |
| 9. C8×D1172 | C2 | semidirect |
| 10. #102×D293 | C2 | semidirect |
| 11. #486×C293 | C2 | semidirect |
| 16. C2×#17989787 | C22 | semidirect |
| 17. C2×C8×D293 | C22 | semidirect |
| 20. #22627599 | C22 | semidirect |
| 26. C4×D1172 | C22 | semidirect |
| 27. C4⋊C4×D293 | C22 | semidirect |
| 28. #22627558 | C22 | semidirect |
| 29. #22627557 | C22 | semidirect |
| 30. C4⋊#14556873 | C22 | semidirect |
| 32. #22627546 | 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 |
| 88. D1172 | D8 | semidirect |
| 89. D1172 | #41 | semidirect |
| 142. C293 | #3294 | semidirect |
| 146. #486 | D293 | semidirect |
| 161. C4⋊Q8 | C2×D293 | semidirect |
| 180. #102 | C2×D293 | semidirect |
| 181. #102 | C2×D293 | semidirect |
| 183. C4×C8 | C2×D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #34036782 | 2 |
| #34036764 | 2 |
| #34036441 | 2 |
| #34036406 | 2 |
| #34036364 | 2 |
| #34036321 | 2 |
| #34036264 | 2 |
| C4×D2344 | 2 |
| C8×D1172 | 2 |
| #102×D293 | 2 |
| #486×C293 | 2 |
| #3294 | 293 |