Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 117 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. #34036836 | C2 | semidirect |
| 2. #34036799 | C2 | semidirect |
| 3. #34036492 | C2 | semidirect |
| 4. #34036475 | C2 | semidirect |
| 5. #34036431 | C2 | semidirect |
| 6. #34036420 | C2 | semidirect |
| 7. #34036322 | C2 | semidirect |
| 8. #34036256 | C2 | semidirect |
| 9. #34036241 | C2 | semidirect |
| 10. C4×#17989787 | C2 | semidirect |
| 11. #459×C293 | C2 | semidirect |
| 97. D4×C293 | #41 | semidirect |
| 129. C293 | #3366 | semidirect |
| 138. #459 | D293 | semidirect |
| 218. D4 | #17989801 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #34036836 | 2 |
| #34036799 | 2 |
| #34036492 | 2 |
| #34036475 | 2 |
| #34036431 | 2 |
| #34036420 | 2 |
| #34036322 | 2 |
| #34036256 | 2 |
| #34036241 | 2 |
| C4×#17989787 | 2 |
| #459×C293 | 2 |
| #3366 | 293 |