Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
274 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 67 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. #14271211 | C2 | semidirect |
| 2. #14271180 | C2 | semidirect |
| 3. #14271168 | C2 | semidirect |
| 4. #14271147 | C2 | semidirect |
| 5. C2×#11745181 | C2 | semidirect |
| 6. #14270935 | C2 | semidirect |
| 135. C29 | #2048 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271211 | 2 |
| #14271180 | 2 |
| #14271168 | 2 |
| #14271147 | 2 |
| C2×#11745181 | 2 |
| #14270935 | 2 |
| C2×C29×AGL(1,ℤ/8) | 2 |
| #2048 | 29 |