Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
408 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 123 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. #14271834 | C2 | semidirect |
| 2. #14271511 | C2 | semidirect |
| 3. #14271487 | C2 | semidirect |
| 4. #14271455 | C2 | semidirect |
| 5. #14271397 | C2 | semidirect |
| 6. #14271358 | C2 | semidirect |
| 7. #14271306 | C2 | semidirect |
| 8. C4×#90783 | C2 | semidirect |
| 9. D4×#6597 | C2 | semidirect |
| 10. #14271157 | C2 | semidirect |
| 11. C29×#555 | C2 | semidirect |
| 127. #555 | D29 | semidirect |
| 173. C29 | #3305 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271834 | 2 |
| #14271511 | 2 |
| #14271487 | 2 |
| #14271455 | 2 |
| #14271397 | 2 |
| #14271358 | 2 |
| #14271306 | 2 |
| C4×#90783 | 2 |
| D4×#6597 | 2 |
| #14271157 | 2 |
| C29×#555 | 2 |
| #3305 | 29 |