Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
698 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 145 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. C2×#22627671 | C2 | semidirect |
| 2. #34036929 | C2 | semidirect |
| 3. #34036927 | C2 | semidirect |
| 4. #34036705 | C2 | semidirect |
| 5. #34036313 | C2 | semidirect |
| 6. #34036303 | C2 | semidirect |
| 7. #34036147 | C2 | semidirect |
| 8. C2×#22627542 | C2 | semidirect |
| 9. #421×C293 | C2 | semidirect |
| 23. #22627657 | C22 | semidirect |
| 25. #22627654 | C22 | semidirect |
| 27. #22627652 | C22 | semidirect |
| 29. #22627649 | C22 | semidirect |
| 33. #22627624 | C22 | semidirect |
| 34. #22627612 | C22 | semidirect |
| 37. #22627552 | C22 | semidirect |
| 38. #22627542 | C22 | semidirect |
| 42. #104×C293 | C22 | semidirect |
| 185. C293 | #3020 | semidirect |
| 194. #421 | D293 | semidirect |
| 227. #104 | C2×D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22627671 | 2 |
| #34036929 | 2 |
| #34036927 | 2 |
| #34036705 | 2 |
| #34036313 | 2 |
| #34036303 | 2 |
| #34036147 | 2 |
| C2×#22627542 | 2 |
| #421×C293 | 2 |
| #3020 | 293 |