Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
392 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 392 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. Q8×Dic586 | C2 | semidirect |
| 3. #34036476 | C2 | semidirect |
| 4. #34036474 | C2 | semidirect |
| 5. #34036419 | C2 | semidirect |
| 6. #34036418 | C2 | semidirect |
| 7. #34036329 | C2 | semidirect |
| 8. #34036327 | C2 | semidirect |
| 9. C8×Dic586 | C2 | semidirect |
| 10. #34036214 | C2 | semidirect |
| 11. C4×SD16×C293 | C2 | semidirect |
| 77. Dic586 | SD16 | semidirect |
| 91. Q8×C293 | #41 | semidirect |
| 125. C293 | #3362 | semidirect |
| 137. C4×SD16 | D293 | semidirect |
| 206. Q8 | #17989802 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic586 | 2 |
| #34036800 | 2 |
| #34036476 | 2 |
| #34036474 | 2 |
| #34036419 | 2 |
| #34036418 | 2 |
| #34036329 | 2 |
| #34036327 | 2 |
| C8×Dic586 | 2 |
| #34036214 | 2 |
| C4×SD16×C293 | 2 |
| #3362 | 293 |