Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
388 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 388 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 |
|---|---|---|
| 2. #34036481 | C2 | semidirect |
| 3. #34036464 | C2 | semidirect |
| 4. #34036421 | C2 | semidirect |
| 5. #34036368 | C2 | semidirect |
| 6. #34036339 | C2 | semidirect |
| 7. #34036284 | C2 | semidirect |
| 8. C4×#17989792 | C2 | semidirect |
| 10. C2×#22627547 | C2 | semidirect |
| 92. D4×C293 | Q16 | semidirect |
| 122. C293 | #3299 | semidirect |
| 208. D4 | #17989792 | 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 |
| #34036464 | 2 |
| #34036421 | 2 |
| #34036368 | 2 |
| #34036339 | 2 |
| #34036284 | 2 |
| C4×#17989792 | 2 |
| D4×#14556873 | 2 |
| C2×#22627547 | 2 |
| #554×C293 | 2 |
| #3299 | 293 |