Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
396 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 396 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 |
|---|---|---|
| 2. #14271511 | C2 | semidirect |
| 3. #14271487 | C2 | semidirect |
| 4. #14271445 | C2 | semidirect |
| 5. #14271394 | C2 | semidirect |
| 6. #14271363 | C2 | semidirect |
| 7. #14271323 | C2 | semidirect |
| 8. C4×#90785 | C2 | semidirect |
| 9. D4×#6597 | C2 | semidirect |
| 10. #14271157 | C2 | semidirect |
| 11. C29×#556 | C2 | semidirect |
| 123. #556 | D29 | semidirect |
| 168. C29 | #3304 | 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 |
| #14271445 | 2 |
| #14271394 | 2 |
| #14271363 | 2 |
| #14271323 | 2 |
| C4×#90785 | 2 |
| D4×#6597 | 2 |
| #14271157 | 2 |
| C29×#556 | 2 |
| #3304 | 29 |