Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
388 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 2. #34036479 | C2 | semidirect |
| 3. #34036462 | C2 | semidirect |
| 4. #34036424 | C2 | semidirect |
| 5. #34036368 | C2 | semidirect |
| 6. #34036336 | C2 | semidirect |
| 7. #34036285 | C2 | semidirect |
| 8. C4×#17989792 | C2 | semidirect |
| 10. C2×#22627548 | C2 | semidirect |
| 92. D4×C293 | Q16 | semidirect |
| 122. C293 | #3299 | semidirect |
| 208. D4 | #17989792 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #34036836 | 2 |
| #34036479 | 2 |
| #34036462 | 2 |
| #34036424 | 2 |
| #34036368 | 2 |
| #34036336 | 2 |
| #34036285 | 2 |
| C4×#17989792 | 2 |
| D4×#14556873 | 2 |
| C2×#22627548 | 2 |
| D4×Q8×C293 | 2 |
| #3299 | 293 |