Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#11745271 | C2 | semidirect |
| 3. #14271734 | C2 | semidirect |
| 4. #14271644 | C2 | semidirect |
| 5. #14271384 | C2 | semidirect |
| 6. #14271377 | C2 | semidirect |
| 7. #14271372 | C2 | semidirect |
| 8. #14271367 | C2 | semidirect |
| 9. #14271191 | C2 | semidirect |
| 10. C2×#11745158 | C2 | semidirect |
| 11. C29×#417 | C2 | semidirect |
| 150. #417 | D29 | semidirect |
| 189. C29 | #3046 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745271 | 2 |
| C2×#11745312 | 2 |
| #14271734 | 2 |
| #14271644 | 2 |
| #14271384 | 2 |
| #14271377 | 2 |
| #14271372 | 2 |
| #14271367 | 2 |
| #14271191 | 2 |
| C2×#11745158 | 2 |
| C29×#417 | 2 |
| #3046 | 29 |