Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
484 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 127 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. C2×#11745281 | C2 | semidirect |
| 2. C2×#11745269 | C2 | semidirect |
| 3. #14271743 | C2 | semidirect |
| 4. #14271418 | C2 | semidirect |
| 5. #14271417 | C2 | semidirect |
| 6. #14271416 | C2 | semidirect |
| 7. #14271395 | C2 | semidirect |
| 8. #14271394 | C2 | semidirect |
| 9. #106×D29 | C2 | semidirect |
| 10. #14271163 | C2 | semidirect |
| 11. C29×#470 | C2 | semidirect |
| 80. C8×D29 | D4 | semidirect |
| 138. #470 | D29 | semidirect |
| 180. C29 | #3060 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745281 | 2 |
| C2×#11745269 | 2 |
| #14271743 | 2 |
| #14271418 | 2 |
| #14271417 | 2 |
| #14271416 | 2 |
| #14271395 | 2 |
| #14271394 | 2 |
| #106×D29 | 2 |
| #14271163 | 2 |
| C29×#470 | 2 |
| #3060 | 29 |