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 |
|---|---|---|
| 1. #14271817 | C2 | semidirect |
| 2. #14271510 | C2 | semidirect |
| 3. #14271359 | C2 | semidirect |
| 4. #14271358 | C2 | semidirect |
| 5. #14270908 | C2 | semidirect |
| 6. #14270892 | C2 | semidirect |
| 7. C29×D4⋊C8 | C2 | semidirect |
| 55. D4×C29 | D8 | semidirect |
| 105. D4⋊C8 | D29 | semidirect |
| 129. C29 | #1625 | semidirect |
| 170. D4 | D232 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271817 | 2 |
| #14271510 | 2 |
| #14271359 | 2 |
| #14271358 | 2 |
| #14270908 | 2 |
| #14270892 | 2 |
| C29×D4⋊C8 | 2 |
| #1625 | 29 |