Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 121 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. #34036666 | C2 | semidirect |
| 2. #34036530 | C2 | semidirect |
| 3. #34036514 | C2 | semidirect |
| 4. #34036485 | C2 | semidirect |
| 5. #34036367 | C2 | semidirect |
| 7. #34036361 | C2 | semidirect |
| 8. C4×#17989789 | C2 | semidirect |
| 9. C4×D2344 | C2 | semidirect |
| 10. C4×C8×D293 | C2 | semidirect |
| 11. C4×Q16×C293 | C2 | semidirect |
| 118. C293 | #3168 | semidirect |
| 127. C4×Q16 | D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #34036666 | 2 |
| #34036530 | 2 |
| #34036514 | 2 |
| #34036485 | 2 |
| #34036367 | 2 |
| #34036366 | 2 |
| #34036361 | 2 |
| C4×#17989789 | 2 |
| C4×D2344 | 2 |
| C4×C8×D293 | 2 |
| C4×Q16×C293 | 2 |
| #3168 | 293 |