Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
484 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 484 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 |
|---|---|---|
| 1. #14271716 | C2 | semidirect |
| 3. #14271526 | C2 | semidirect |
| 4. #14271508 | C2 | semidirect |
| 5. #14271169 | C2 | semidirect |
| 6. #14271168 | C2 | semidirect |
| 7. #14271167 | C2 | semidirect |
| 8. M16×Dic29 | C2 | semidirect |
| 9. C29×#418 | C2 | semidirect |
| 21. #11745252 | C22 | semidirect |
| 22. #11745250 | C22 | semidirect |
| 25. C29×#102 | C22 | semidirect |
| 26. #11745180 | C22 | semidirect |
| 27. #11745169 | C22 | semidirect |
| 28. #11745163 | C22 | semidirect |
| 29. C8×Dic29 | C22 | semidirect |
| 30. #11745157 | C22 | semidirect |
| 114. #418 | D29 | semidirect |
| 139. #102 | C2×D29 | semidirect |
| 142. C29 | #3138 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271716 | 2 |
| C2×#11745302 | 2 |
| #14271526 | 2 |
| #14271508 | 2 |
| #14271169 | 2 |
| #14271168 | 2 |
| #14271167 | 2 |
| M16×Dic29 | 2 |
| C29×#418 | 2 |
| #3138 | 29 |