Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
234 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 59 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. #14271566 | C2 | semidirect |
| 3. #14271370 | C2 | semidirect |
| 4. #14270908 | C2 | semidirect |
| 5. #14270893 | C2 | semidirect |
| 54. D4×C29 | Q16 | semidirect |
| 117. C29 | #1649 | semidirect |
| 152. D4 | #90785 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic58 | 2 |
| #14271566 | 2 |
| #14271370 | 2 |
| #14270908 | 2 |
| #14270893 | 2 |
| D4⋊#6597 | 2 |
| C29×#474 | 2 |
| #1649 | 29 |