Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
738 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 157 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. C23×Dic58 | C2 | semidirect |
| 2. C2×#11745313 | C2 | semidirect |
| 3. #14271318 | C2 | semidirect |
| 4. #14271301 | C2 | semidirect |
| 5. #14271171 | C2 | semidirect |
| 6. #14271127 | C2 | semidirect |
| 23. C2×#90785 | C22 | semidirect |
| 24. C2×#90783 | C22 | semidirect |
| 27. #11745158 | C22 | semidirect |
| 49. C2×Dic58 | D4 | semidirect |
| 96. C22×C29 | #137 | semidirect |
| 136. C29 | #3004 | semidirect |
| 204. C22 | #11745313 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic58 | 2 |
| C2×#11745313 | 2 |
| #14271318 | 2 |
| #14271301 | 2 |
| #14271171 | 2 |
| #14271127 | 2 |
| C29×#525 | 2 |
| #3004 | 29 |