Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
426 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 91 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. C22×#90783 | C2 | semidirect |
| 2. C2×#11745298 | C2 | semidirect |
| 3. C2×#11745164 | C2 | semidirect |
| 4. C2×#11745180 | C2 | semidirect |
| 5. #14271066 | C2 | semidirect |
| 6. #14270917 | C2 | semidirect |
| 160. C29 | #2012 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90783 | 2 |
| C2×#11745298 | 2 |
| C2×#11745164 | 2 |
| C2×#11745180 | 2 |
| #14271066 | 2 |
| #14270917 | 2 |
| C22×D8×C29 | 2 |
| #2012 | 29 |