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 |
| 3. #34036480 | C2 | semidirect |
| 4. #34036460 | C2 | semidirect |
| 5. #34036415 | C2 | semidirect |
| 6. #34036358 | C2 | semidirect |
| 7. #34036335 | C2 | semidirect |
| 8. #34036270 | C2 | semidirect |
| 9. C4×#17989791 | C2 | semidirect |
| 10. C2×#22627549 | C2 | semidirect |
| 11. C8×D4×C293 | C2 | semidirect |
| 83. Dic586 | #41 | semidirect |
| 96. D4×C293 | SD16 | semidirect |
| 128. C293 | #3298 | semidirect |
| 139. C8×D4 | D293 | semidirect |
| 217. D4 | #17989791 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic586 | 2 |
| #34036783 | 2 |
| #34036480 | 2 |
| #34036460 | 2 |
| #34036415 | 2 |
| #34036358 | 2 |
| #34036335 | 2 |
| #34036270 | 2 |
| C4×#17989791 | 2 |
| C2×#22627549 | 2 |
| C8×D4×C293 | 2 |
| #3298 | 293 |