Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
256 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 2. C2×#11745167 | C2 | semidirect |
| 3. #14270977 | C2 | direct (N × H) |
| 4. C2×C29×M32 | C2 | semidirect |
| 15. C29×M32 | C22 | semidirect |
| 18. #11745167 | C22 | semidirect |
| 75. C2×M32 | D29 | semidirect |
| 80. C2×C29 | #361 | semidirect |
| 93. M32 | C2×D29 | semidirect |
| 97. C29 | C2×#361 | semidirect |
| 155. C2 | #14270977 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D232 | 2 |
| C2×#11745167 | 2 |
| #14270977 | 2 |
| C2×C29×M32 | 2 |
| C2×#361 | 29 |