Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 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. #34036660 | C2 | semidirect |
| 2. #34036530 | C2 | semidirect |
| 3. #34036512 | C2 | semidirect |
| 4. #34036482 | C2 | semidirect |
| 5. #34036370 | C2 | semidirect |
| 6. #34036356 | C2 | semidirect |
| 7. #34036223 | C2 | semidirect |
| 8. #34036220 | C2 | semidirect |
| 9. D8×Dic293 | C2 | semidirect |
| 10. C2×C8×Dic293 | C2 | semidirect |
| 118. C293 | #3168 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #34036660 | 2 |
| #34036530 | 2 |
| #34036512 | 2 |
| #34036482 | 2 |
| #34036370 | 2 |
| #34036356 | 2 |
| #34036223 | 2 |
| #34036220 | 2 |
| D8×Dic293 | 2 |
| C2×C8×Dic293 | 2 |
| #466×C293 | 2 |
| #3168 | 293 |