Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
444 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 444 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. #34036681 | C2 | semidirect |
| 3. #34036465 | C2 | semidirect |
| 4. #34036462 | C2 | semidirect |
| 5. #34036407 | C2 | semidirect |
| 6. #34036332 | C2 | semidirect |
| 8. #34036230 | C2 | semidirect |
| 9. #34036226 | C2 | semidirect |
| 10. #34036183 | C2 | semidirect |
| 14. #22627623 | C22 | semidirect |
| 15. #22627622 | C22 | semidirect |
| 19. Q8×Dic293 | C22 | semidirect |
| 21. #22627589 | C22 | semidirect |
| 30. #22627558 | C22 | semidirect |
| 31. #22627557 | C22 | semidirect |
| 32. #22627553 | C22 | semidirect |
| 33. #22627549 | C22 | semidirect |
| 34. #22627548 | C22 | semidirect |
| 37. #22627534 | C22 | semidirect |
| 136. C293 | #3110 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #34036681 | 2 |
| C2×D4×Dic293 | 2 |
| #34036465 | 2 |
| #34036462 | 2 |
| #34036407 | 2 |
| #34036332 | 2 |
| #34036280 | 2 |
| #34036230 | 2 |
| #34036226 | 2 |
| #34036183 | 2 |
| #450×C293 | 2 |
| #3110 | 293 |