Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
278 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 65 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. #14271789 | C2 | semidirect |
| 4. #14270930 | C2 | semidirect |
| 5. #14270929 | C2 | semidirect |
| 6. #14270929 | C2 | semidirect |
| 21. C24×C29 | Q8 | semidirect |
| 31. C22×C4×C29 | Q8 | semidirect |
| 138. C29 | #2032 | semidirect |
| 139. C24 | Dic58 | semidirect |
| 154. C22×C4 | Dic58 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271789 | 2 |
| C2×#11745182 | 2 |
| #14270930 | 2 |
| #14270929 | 2 |
| C2×C29×#99 | 2 |
| #2032 | 29 |