Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
180 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 180 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 |
|---|---|---|
| 1. C8×Dic58 | C2 | semidirect |
| 3. #14270913 | C2 | semidirect |
| 4. #14270893 | C2 | semidirect |
| 6. C8×#6597 | C2 | semidirect |
| 33. #90783 | C8 | direct (N × H) |
| 53. Dic58 | C2×C8 | semidirect |
| 56. C8×C29 | SD16 | semidirect |
| 60. #6597 | C2×C8 | semidirect |
| 100. C29 | C8×SD16 | semidirect |
| 138. C8 | #90783 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×Dic58 | 2 |
| C4×#90783 | 2 |
| #14270913 | 2 |
| #14270893 | 2 |
| D4⋊#6597 | 2 |
| C8×#6597 | 2 |
| C8×D4×C29 | 2 |
| C8×SD16 | 29 |