Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
216 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 53 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. #14271603 | C2 | semidirect |
| 2. C2×#11745175 | C2 | semidirect |
| 3. #14271438 | C2 | semidirect |
| 4. #14270976 | C2 | semidirect |
| 5. #14270970 | C2 | semidirect |
| 6. #14270947 | C2 | semidirect |
| 17. C2×Dic116 | C22 | semidirect |
| 22. #11745167 | C22 | semidirect |
| 23. #11745160 | C22 | semidirect |
| 24. C2×#90768 | C22 | semidirect |
| 116. C29 | #2194 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271603 | 2 |
| C2×#11745175 | 2 |
| #14271438 | 2 |
| #14270976 | 2 |
| #14270970 | 2 |
| #14270947 | 2 |
| C29×#576 | 2 |
| #2194 | 29 |