Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
400 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 125 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. #14271524 | C2 | semidirect |
| 4. #14271519 | C2 | semidirect |
| 5. #14271172 | C2 | semidirect |
| 8. M16×Dic29 | C2 | semidirect |
| 9. C29×#419 | C2 | semidirect |
| 21. #11745252 | C22 | semidirect |
| 22. #11745250 | C22 | semidirect |
| 25. C29×#103 | C22 | semidirect |
| 26. #11745183 | C22 | semidirect |
| 28. #11745163 | C22 | semidirect |
| 29. C8×Dic29 | C22 | semidirect |
| 106. #419 | D29 | semidirect |
| 130. #103 | C2×D29 | semidirect |
| 135. C29 | #3140 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271716 | 2 |
| C2×#11745309 | 2 |
| #14271524 | 2 |
| #14271519 | 2 |
| #14271172 | 2 |
| #14271169 | 2 |
| #14271167 | 2 |
| M16×Dic29 | 2 |
| C29×#419 | 2 |
| #3140 | 29 |