Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
388 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 388 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 |
|---|---|---|
| 3. #34036481 | C2 | semidirect |
| 4. #34036466 | C2 | semidirect |
| 5. #34036371 | C2 | semidirect |
| 6. #34036340 | C2 | semidirect |
| 7. #34036286 | C2 | semidirect |
| 8. C4×#17989792 | C2 | semidirect |
| 10. #103×D293 | C2 | semidirect |
| 11. #477×C293 | C2 | semidirect |
| 82. D1172 | Q16 | semidirect |
| 122. C293 | #3299 | semidirect |
| 128. #477 | D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #34036840 | 2 |
| Q8×D1172 | 2 |
| #34036481 | 2 |
| #34036466 | 2 |
| #34036371 | 2 |
| #34036340 | 2 |
| #34036286 | 2 |
| C4×#17989792 | 2 |
| #34036194 | 2 |
| #103×D293 | 2 |
| #477×C293 | 2 |
| #3299 | 293 |