Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
320 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 3. C4×#17989786 | C2 | semidirect |
| 4. #34035889 | C2 | semidirect |
| 5. #376×C293 | C2 | semidirect |
| 8. C4×Dic586 | C4 | semidirect |
| 9. C4×D1172 | C4 | semidirect |
| 14. #22627552 | C4 | semidirect |
| 28. #17989786 | C2×C4 | semidirect |
| 41. C42×C293 | C2×C4 | semidirect |
| 82. C293 | #1759 | semidirect |
| 87. #376 | D293 | semidirect |
| 124. C42 | C4×D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#17989802 | 2 |
| C2×#22627552 | 2 |
| C4×#17989786 | 2 |
| #34035889 | 2 |
| #376×C293 | 2 |
| #1759 | 293 |