Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
408 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 408 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 |
|---|---|---|
| 1. #34036844 | C2 | semidirect |
| 2. #34036475 | C2 | semidirect |
| 3. #34036450 | C2 | semidirect |
| 4. #34036424 | C2 | semidirect |
| 5. #34036363 | C2 | semidirect |
| 6. #34036321 | C2 | semidirect |
| 7. #34036274 | C2 | semidirect |
| 8. C4×#17989789 | C2 | semidirect |
| 9. D4×#14556873 | C2 | semidirect |
| 10. #34036125 | C2 | semidirect |
| 11. #550×C293 | C2 | semidirect |
| 132. C293 | #3305 | semidirect |
| 135. #550 | D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #34036844 | 2 |
| #34036475 | 2 |
| #34036450 | 2 |
| #34036424 | 2 |
| #34036363 | 2 |
| #34036321 | 2 |
| #34036274 | 2 |
| C4×#17989789 | 2 |
| D4×#14556873 | 2 |
| #34036125 | 2 |
| #550×C293 | 2 |
| #3305 | 293 |