Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
336 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 336 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. #34036433 | C2 | semidirect |
| 7. #34036339 | C2 | semidirect |
| 8. Q8×#14556873 | C2 | semidirect |
| 9. C4×#17989792 | C2 | semidirect |
| 11. #557×C293 | C2 | semidirect |
| 115. C293 | #3364 | semidirect |
| 117. #557 | D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #34036852 | 2 |
| #34036486 | 2 |
| #34036481 | 2 |
| #34036433 | 2 |
| #34036406 | 2 |
| #34036351 | 2 |
| #34036339 | 2 |
| Q8×#14556873 | 2 |
| C4×#17989792 | 2 |
| C4×#17989789 | 2 |
| #557×C293 | 2 |
| #3364 | 293 |