Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
350 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 350 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. #34036852 | C2 | semidirect |
| 2. #34036839 | C2 | semidirect |
| 3. #34036484 | C2 | semidirect |
| 4. #34036480 | C2 | semidirect |
| 5. #34036437 | C2 | semidirect |
| 6. #34036420 | C2 | semidirect |
| 8. #34036335 | C2 | semidirect |
| 9. C4×#17989791 | C2 | semidirect |
| 11. C8×Q8×C293 | C2 | semidirect |
| 120. C293 | #3360 | semidirect |
| 130. C8×Q8 | D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #34036852 | 2 |
| #34036839 | 2 |
| #34036484 | 2 |
| #34036480 | 2 |
| #34036437 | 2 |
| #34036420 | 2 |
| #34036345 | 2 |
| #34036335 | 2 |
| C4×#17989791 | 2 |
| C4×D2344 | 2 |
| C8×Q8×C293 | 2 |
| #3360 | 293 |