Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
488 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 488 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. #34036677 | C2 | semidirect |
| 2. C4×D4×D293 | C2 | semidirect |
| 3. #34036446 | C2 | semidirect |
| 4. #34036420 | C2 | semidirect |
| 5. #34036419 | C2 | semidirect |
| 6. #34036321 | C2 | semidirect |
| 7. #34036261 | C2 | semidirect |
| 8. #34036241 | C2 | semidirect |
| 9. #34036238 | C2 | semidirect |
| 10. #34036185 | C2 | semidirect |
| 11. #459×C293 | C2 | semidirect |
| 16. #22627624 | C22 | semidirect |
| 23. D4×Dic293 | C22 | semidirect |
| 30. #22627556 | C22 | semidirect |
| 31. #22627555 | C22 | semidirect |
| 32. C4⋊#14556873 | C22 | semidirect |
| 35. #22627545 | C22 | semidirect |
| 37. #22627534 | C22 | semidirect |
| 39. #127×C293 | C22 | semidirect |
| 41. C4⋊C8×C293 | C22 | semidirect |
| 42. #102×C293 | C22 | semidirect |
| 91. D1172 | #41 | semidirect |
| 116. D4×C293 | #41 | semidirect |
| 154. C293 | #3109 | semidirect |
| 162. #459 | D293 | semidirect |
| 173. #127 | C2×D293 | semidirect |
| 191. C4⋊C8 | C2×D293 | semidirect |
| 195. #102 | C2×D293 | semidirect |
| 256. D4 | #17989801 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #34036677 | 2 |
| C4×D4×D293 | 2 |
| #34036446 | 2 |
| #34036420 | 2 |
| #34036419 | 2 |
| #34036321 | 2 |
| #34036261 | 2 |
| #34036241 | 2 |
| #34036238 | 2 |
| #34036185 | 2 |
| #459×C293 | 2 |
| #3109 | 293 |