Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
142 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 51 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. #14271567 | C2 | semidirect |
| 3. #14270991 | C2 | semidirect |
| 4. #14270990 | C2 | semidirect |
| 5. #14270981 | C2 | semidirect |
| 23. D8×C29 | Q8 | semidirect |
| 82. C29 | #2226 | semidirect |
| 87. D8 | Dic58 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271567 | 2 |
| D8×Dic29 | 2 |
| #14270991 | 2 |
| #14270990 | 2 |
| #14270981 | 2 |
| #14270964 | 2 |
| C29×#357 | 2 |
| #2226 | 29 |