Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
390 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 129 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. C2×C4×Dic58 | C2 | semidirect |
| 3. #14271494 | C2 | semidirect |
| 5. #14271471 | C2 | semidirect |
| 6. #14271386 | C2 | semidirect |
| 7. #14271321 | C2 | semidirect |
| 9. C4×Dic116 | C2 | semidirect |
| 10. C4×#90773 | C2 | semidirect |
| 11. C29×#431 | C2 | semidirect |
| 137. #431 | D29 | semidirect |
| 174. C29 | #3108 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271697 | 2 |
| C2×C4×Dic58 | 2 |
| #14271494 | 2 |
| #14271477 | 2 |
| #14271471 | 2 |
| #14271386 | 2 |
| #14271321 | 2 |
| #14271304 | 2 |
| C4×Dic116 | 2 |
| C4×#90773 | 2 |
| C29×#431 | 2 |
| #3108 | 29 |