Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
760 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 165 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×#11745313 | C2 | semidirect |
| 2. C2×#11745298 | C2 | semidirect |
| 3. #14271341 | C2 | direct (N × H) |
| 4. C2×#11745185 | C2 | semidirect |
| 5. C2×#11745181 | C2 | semidirect |
| 15. C22×Dic58 | C22 | semidirect |
| 18. #11745313 | C22 | semidirect |
| 21. #11745298 | C22 | semidirect |
| 23. C2×C4×Dic29 | C22 | semidirect |
| 24. C2×#90777 | C22 | semidirect |
| 25. #11745185 | C22 | semidirect |
| 26. #11745181 | C22 | semidirect |
| 55. C2×Dic58 | C23 | semidirect |
| 60. C4×Dic29 | C23 | semidirect |
| 62. #90777 | C23 | semidirect |
| 124. C2×C29 | #455 | semidirect |
| 146. C29 | C2×#455 | semidirect |
| 237. C2 | #14271341 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745313 | 2 |
| C2×#11745298 | 2 |
| #14271341 | 2 |
| C2×#11745185 | 2 |
| C2×#11745181 | 2 |
| C2×C29×H(5,𝔽2) | 2 |
| C2×#455 | 29 |