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. #14271713 | C2 | semidirect |
| 2. #14271573 | C2 | semidirect |
| 3. #14271553 | C2 | semidirect |
| 4. #14271529 | C2 | semidirect |
| 5. #14271522 | C2 | semidirect |
| 6. #14271414 | C2 | semidirect |
| 7. #14271411 | C2 | semidirect |
| 8. C4×#90784 | C2 | semidirect |
| 9. C4×#90782 | C2 | semidirect |
| 10. C4×#90777 | C2 | semidirect |
| 11. C29×#529 | C2 | semidirect |
| 110. #6597 | #41 | semidirect |
| 133. #529 | 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 |
|---|---|
| #14271713 | 2 |
| #14271573 | 2 |
| #14271553 | 2 |
| #14271529 | 2 |
| #14271522 | 2 |
| #14271414 | 2 |
| #14271411 | 2 |
| C4×#90784 | 2 |
| C4×#90782 | 2 |
| C4×#90777 | 2 |
| C29×#529 | 2 |
| #3171 | 29 |