Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
104 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 35 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. Q32×D29 | C2 | semidirect |
| 3. Dic464 | C2 | semidirect |
| 4. #14271003 | C2 | semidirect |
| 5. #14271001 | C2 | semidirect |
| 6. #14270996 | C2 | semidirect |
| 7. C29×SD64 | C2 | semidirect |
| 54. SD64 | D29 | semidirect |
| 70. C29 | #2264 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271592 | 2 |
| Q32×D29 | 2 |
| Dic464 | 2 |
| #14271003 | 2 |
| #14271001 | 2 |
| #14270996 | 2 |
| C29×SD64 | 2 |
| #2264 | 29 |