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. #14271976 | C2 | semidirect |
| 3. #14271606 | C2 | semidirect |
| 4. #14271605 | C2 | semidirect |
| 5. #14271602 | C2 | semidirect |
| 6. #14271594 | C2 | semidirect |
| 7. #14271593 | C2 | semidirect |
| 8. C2×#11745177 | C2 | semidirect |
| 9. Q32×D29 | C2 | semidirect |
| 10. #14271581 | C2 | semidirect |
| 11. C29×#510 | C2 | semidirect |
| 124. #510 | D29 | semidirect |
| 164. C29 | #3417 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271977 | 2 |
| #14271976 | 2 |
| #14271606 | 2 |
| #14271605 | 2 |
| #14271602 | 2 |
| #14271594 | 2 |
| #14271593 | 2 |
| C2×#11745177 | 2 |
| Q32×D29 | 2 |
| #14271581 | 2 |
| C29×#510 | 2 |
| #3417 | 29 |