Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
430 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 430 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. #34036679 | C2 | semidirect |
| 2. C4×#17989802 | C2 | semidirect |
| 3. #34036454 | C2 | semidirect |
| 4. #34036415 | C2 | semidirect |
| 5. #34036410 | C2 | semidirect |
| 6. #34036330 | C2 | semidirect |
| 7. #34036325 | C2 | semidirect |
| 8. #34036276 | C2 | semidirect |
| 9. #34036242 | C2 | semidirect |
| 10. #34036231 | C2 | semidirect |
| 11. #432×C293 | C2 | semidirect |
| 87. Dic586 | #41 | semidirect |
| 93. D1172 | #41 | semidirect |
| 144. C293 | #3115 | semidirect |
| 156. #432 | D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #34036679 | 2 |
| C4×#17989802 | 2 |
| #34036454 | 2 |
| #34036415 | 2 |
| #34036410 | 2 |
| #34036330 | 2 |
| #34036325 | 2 |
| #34036276 | 2 |
| #34036242 | 2 |
| #34036231 | 2 |
| #432×C293 | 2 |
| #3115 | 293 |