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. #34036475 | C2 | semidirect |
| 4. #34036474 | C2 | semidirect |
| 5. #34036420 | C2 | semidirect |
| 6. #34036417 | C2 | semidirect |
| 7. #34036327 | C2 | semidirect |
| 8. #34036253 | C2 | semidirect |
| 9. SD16×Dic293 | C2 | semidirect |
| 10. C4×#17989789 | C2 | semidirect |
| 11. #460×C293 | C2 | semidirect |
| 77. Dic586 | SD16 | semidirect |
| 92. Q8×C293 | #41 | semidirect |
| 125. C293 | #3362 | semidirect |
| 134. #460 | D293 | semidirect |
| 206. Q8 | #17989801 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic586 | 2 |
| #34036799 | 2 |
| #34036475 | 2 |
| #34036474 | 2 |
| #34036420 | 2 |
| #34036417 | 2 |
| #34036327 | 2 |
| #34036253 | 2 |
| SD16×Dic293 | 2 |
| C4×#17989789 | 2 |
| #460×C293 | 2 |
| #3362 | 293 |