Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
164 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 164 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 |
|---|---|---|
| 27. Dic116 | C8 | direct (N × H) |
| 39. C8×C29 | Q16 | semidirect |
| 68. C29 | C8×Q16 | semidirect |
| 93. C8 | Dic116 | 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×Dic116 | 2 |
| #14270916 | 2 |
| #14270895 | 2 |
| C82×C29 | 2 |
| C8×Q16 | 29 |