Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
756 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 756 conjugacy classes of subgroups — too many to draw. Only its 202 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×#90800 | C2 | semidirect |
| 2. #14272150 | C2 | direct (N × H) |
| 3. C2×#11745221 | C2 | semidirect |
| 4. C2×#11745229 | C2 | semidirect |
| 21. C2×#90800 | C22 | semidirect |
| 23. #11745229 | C22 | semidirect |
| 24. #11745221 | C22 | semidirect |
| 142. C2×C29 | #413 | semidirect |
| 164. C29 | C2×#413 | semidirect |
| 277. C2 | #14272150 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90800 | 2 |
| #14272150 | 2 |
| C2×#11745221 | 2 |
| C2×#11745229 | 2 |
| C22×#90807 | 2 |
| C2×#413 | 29 |