Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
364 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 129 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. #34036686 | C2 | semidirect |
| 3. #34036538 | C2 | semidirect |
| 4. #34036523 | C2 | semidirect |
| 5. #34036498 | C2 | semidirect |
| 6. #34036489 | C2 | semidirect |
| 7. #34036387 | C2 | semidirect |
| 9. C4×Dic1172 | C2 | semidirect |
| 10. C4×#17989791 | C2 | semidirect |
| 11. C4×M16×C293 | C2 | semidirect |
| 129. C293 | #3172 | semidirect |
| 141. C4×M16 | D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #34036686 | 2 |
| #34036663 | 2 |
| #34036538 | 2 |
| #34036523 | 2 |
| #34036498 | 2 |
| #34036489 | 2 |
| #34036387 | 2 |
| #34036375 | 2 |
| C4×Dic1172 | 2 |
| C4×#17989791 | 2 |
| C4×M16×C293 | 2 |
| #3172 | 293 |