Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
172 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 172 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. #14271449 | C2 | semidirect |
| 4. C8×Dic58 | C2 | semidirect |
| 5. #14270908 | C2 | semidirect |
| 7. C29×#334 | C2 | semidirect |
| 57. Dic58 | SD16 | semidirect |
| 61. C8×C29 | SD16 | semidirect |
| 80. #334 | D29 | semidirect |
| 102. C29 | #1666 | semidirect |
| 142. C8 | #90773 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271536 | 2 |
| #14271449 | 2 |
| #14271364 | 2 |
| C8×Dic58 | 2 |
| #14270908 | 2 |
| #14270906 | 2 |
| C29×#334 | 2 |
| #1666 | 29 |