Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
256 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 57 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. #14271537 | C2 | semidirect |
| 3. #14271450 | C2 | semidirect |
| 4. #14270906 | C2 | semidirect |
| 5. Q8⋊#6597 | C2 | semidirect |
| 6. #14270890 | C2 | semidirect |
| 7. C29×#477 | C2 | semidirect |
| 54. Q8×C29 | SD16 | semidirect |
| 96. #477 | D29 | semidirect |
| 123. C29 | #1631 | semidirect |
| 153. Q8 | #90784 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271835 | 2 |
| #14271537 | 2 |
| #14271450 | 2 |
| #14270906 | 2 |
| Q8⋊#6597 | 2 |
| #14270890 | 2 |
| C29×#477 | 2 |
| #1631 | 29 |