Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
612 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 197 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. C2×#22627589 | C2 | semidirect |
| 4. #34036035 | C2 | semidirect |
| 5. #34036023 | C2 | semidirect |
| 6. #34036001 | C2 | semidirect |
| 7. #34035998 | C2 | semidirect |
| 8. #34035975 | C2 | semidirect |
| 12. #22627611 | C4 | semidirect |
| 32. C2×Dic586 | C2×C4 | semidirect |
| 44. C22⋊Dic293 | C2×C4 | semidirect |
| 46. C4×Dic293 | C2×C4 | semidirect |
| 111. C293 | #2326 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22627611 | 2 |
| C2×#22627589 | 2 |
| C2×D4×Dic293 | 2 |
| #34036035 | 2 |
| #34036023 | 2 |
| #34036001 | 2 |
| #34035998 | 2 |
| #34035975 | 2 |
| #390×C293 | 2 |
| #2326 | 293 |