Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
390 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 101 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×#90777 | C2 | semidirect |
| 2. C2×#11745181 | C2 | semidirect |
| 3. #14271127 | C2 | semidirect |
| 4. #14270932 | C2 | semidirect |
| 49. #90777 | D4 | semidirect |
| 98. C22×C29 | #100 | semidirect |
| 136. C29 | #1900 | semidirect |
| 211. C22 | #11745181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90777 | 2 |
| C2×#11745181 | 2 |
| #14271127 | 2 |
| #14270932 | 2 |
| C2×C29×#121 | 2 |
| #1900 | 29 |