Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
236 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 77 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. M32×D29 | C2 | semidirect |
| 3. #14270945 | C2 | semidirect |
| 4. #14270944 | C2 | semidirect |
| 5. C29×#349 | C2 | semidirect |
| 15. C29×M32 | C22 | semidirect |
| 16. #11745160 | C22 | semidirect |
| 93. #349 | D29 | direct (N × H) |
| 99. D29 | #349 | direct (N × H) |
| 111. M32 | C2×D29 | semidirect |
| 113. C29 | C2×#349 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M16×D29 | 2 |
| M32×D29 | 2 |
| #14270945 | 2 |
| #14270944 | 2 |
| C29×#349 | 2 |
| C2×#349 | 29 |