Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
408 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 408 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. #14271697 | C2 | semidirect |
| 2. #14271569 | C2 | semidirect |
| 3. #14271550 | C2 | semidirect |
| 4. #14271527 | C2 | semidirect |
| 5. #14271525 | C2 | semidirect |
| 6. #14271414 | C2 | semidirect |
| 7. #14271407 | C2 | semidirect |
| 8. C4×#90783 | C2 | semidirect |
| 9. C4×#90782 | C2 | semidirect |
| 10. C4×#90777 | C2 | semidirect |
| 11. C29×#532 | C2 | semidirect |
| 110. #6597 | #41 | semidirect |
| 132. #532 | D29 | semidirect |
| 180. C29 | #3171 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271697 | 2 |
| #14271569 | 2 |
| #14271550 | 2 |
| #14271527 | 2 |
| #14271525 | 2 |
| #14271414 | 2 |
| #14271407 | 2 |
| C4×#90783 | 2 |
| C4×#90782 | 2 |
| C4×#90777 | 2 |
| C29×#532 | 2 |
| #3171 | 29 |