Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
420 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 139 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. D4×Dic586 | C2 | semidirect |
| 2. #34036481 | C2 | semidirect |
| 3. #34036459 | C2 | semidirect |
| 4. #34036411 | C2 | semidirect |
| 5. #34036356 | C2 | semidirect |
| 6. #34036334 | C2 | semidirect |
| 7. #34036267 | C2 | semidirect |
| 8. C4×#17989790 | C2 | semidirect |
| 9. D4×#14556873 | C2 | semidirect |
| 10. C2×#22627547 | C2 | semidirect |
| 81. Dic586 | #41 | semidirect |
| 95. D4×C293 | SD16 | semidirect |
| 128. C293 | #3298 | semidirect |
| 217. D4 | #17989790 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic586 | 2 |
| #34036481 | 2 |
| #34036459 | 2 |
| #34036411 | 2 |
| #34036356 | 2 |
| #34036334 | 2 |
| #34036267 | 2 |
| C4×#17989790 | 2 |
| D4×#14556873 | 2 |
| C2×#22627547 | 2 |
| #547×C293 | 2 |
| #3298 | 293 |