Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
484 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 125 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. #34036684 | C2 | semidirect |
| 3. #34036492 | C2 | semidirect |
| 4. #34036477 | C2 | semidirect |
| 5. #34036476 | C2 | semidirect |
| 6. #34036475 | C2 | semidirect |
| 7. #34036132 | C2 | semidirect |
| 8. C4×#17989785 | C2 | semidirect |
| 9. #486×C293 | C2 | semidirect |
| 14. #22627624 | C22 | semidirect |
| 19. #22627615 | C22 | semidirect |
| 26. #22627546 | C22 | semidirect |
| 27. #22627545 | C22 | semidirect |
| 28. #22627544 | C22 | semidirect |
| 29. #22627534 | C22 | semidirect |
| 30. C4×#14556873 | C22 | semidirect |
| 31. C4⋊Q8×C293 | C22 | semidirect |
| 33. #102×C293 | C22 | semidirect |
| 34. C4×C8×C293 | C22 | semidirect |
| 123. C293 | #3138 | semidirect |
| 131. #486 | D293 | semidirect |
| 139. C4⋊Q8 | C2×D293 | semidirect |
| 155. #102 | C2×D293 | semidirect |
| 158. C4×C8 | C2×D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #34036684 | 2 |
| #127×D293 | 2 |
| #34036492 | 2 |
| #34036477 | 2 |
| #34036476 | 2 |
| #34036475 | 2 |
| #34036132 | 2 |
| C4×#17989785 | 2 |
| #486×C293 | 2 |
| #3138 | 293 |