Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
350 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 113 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. #14271977 | C2 | semidirect |
| 2. #14271603 | C2 | semidirect |
| 3. #14271602 | C2 | semidirect |
| 4. #14271592 | C2 | semidirect |
| 5. C2×Dic232 | C2 | semidirect |
| 6. Q32×D29 | C2 | semidirect |
| 7. #14271579 | C2 | semidirect |
| 8. C29×#508 | C2 | semidirect |
| 82. #508 | D29 | semidirect |
| 109. C29 | #3417 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271977 | 2 |
| #14271603 | 2 |
| #14271602 | 2 |
| #14271592 | 2 |
| C2×Dic232 | 2 |
| Q32×D29 | 2 |
| #14271579 | 2 |
| C29×#508 | 2 |
| #3417 | 29 |