Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
484 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 127 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×#11745274 | C2 | semidirect |
| 2. C2×#11745269 | C2 | semidirect |
| 3. #14271742 | C2 | semidirect |
| 4. #14271422 | C2 | semidirect |
| 5. #14271421 | C2 | semidirect |
| 6. #14271413 | C2 | semidirect |
| 7. #14271391 | C2 | semidirect |
| 8. #14271390 | C2 | semidirect |
| 9. #106×D29 | C2 | semidirect |
| 10. #14271161 | C2 | semidirect |
| 11. C29×#469 | C2 | semidirect |
| 80. C8×D29 | D4 | semidirect |
| 140. #469 | D29 | semidirect |
| 180. C29 | #3060 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745274 | 2 |
| C2×#11745269 | 2 |
| #14271742 | 2 |
| #14271422 | 2 |
| #14271421 | 2 |
| #14271413 | 2 |
| #14271391 | 2 |
| #14271390 | 2 |
| #106×D29 | 2 |
| #14271161 | 2 |
| C29×#469 | 2 |
| #3060 | 29 |