Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
370 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 125 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. #14271891 | C2 | semidirect |
| 3. #14271514 | C2 | semidirect |
| 4. #14271512 | C2 | semidirect |
| 5. #14271448 | C2 | semidirect |
| 6. #14271447 | C2 | semidirect |
| 9. C8×Dic58 | C2 | semidirect |
| 95. Dic58 | SD16 | semidirect |
| 159. C29 | #3359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271891 | 2 |
| D4×Dic58 | 2 |
| #14271514 | 2 |
| #14271512 | 2 |
| #14271448 | 2 |
| #14271447 | 2 |
| #14271368 | 2 |
| #14271366 | 2 |
| C8×Dic58 | 2 |
| #14271254 | 2 |
| C4×SD16×C29 | 2 |
| #3359 | 29 |