Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
188 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 188 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 |
|---|---|---|
| 1. #14271536 | C2 | semidirect |
| 2. #14271444 | C2 | semidirect |
| 4. C8×D116 | C2 | semidirect |
| 5. #14270908 | C2 | semidirect |
| 6. #14270906 | C2 | semidirect |
| 7. C29×#334 | C2 | semidirect |
| 56. D116 | SD16 | semidirect |
| 64. C8×C29 | D8 | semidirect |
| 85. #334 | D29 | semidirect |
| 108. C29 | #1665 | semidirect |
| 151. C8 | D232 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271536 | 2 |
| #14271444 | 2 |
| #14271359 | 2 |
| C8×D116 | 2 |
| #14270908 | 2 |
| #14270906 | 2 |
| C29×#334 | 2 |
| #1665 | 29 |