Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
154 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 55 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×#11745177 | C2 | semidirect |
| 4. #14270988 | C2 | semidirect |
| 5. #14270967 | C2 | semidirect |
| 6. #14270966 | C2 | semidirect |
| 59. C22×C29 | Q32 | semidirect |
| 92. C29 | #2216 | semidirect |
| 130. C22 | #11745177 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745177 | 2 |
| C22×#90768 | 2 |
| #14271404 | 2 |
| #14270988 | 2 |
| #14270967 | 2 |
| #14270966 | 2 |
| C29×#467 | 2 |
| #2216 | 29 |