Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
260 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 16. #11745252 | C4 | semidirect |
| 17. #11745252 | C4 | semidirect |
| 18. #11745250 | C4 | semidirect |
| 19. #11745250 | C4 | semidirect |
| 35. M16×C29 | Q8 | semidirect |
| 61. #90777 | Q8 | semidirect |
| 141. C29 | #1986 | semidirect |
| 152. M16 | Dic58 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271716 | 2 |
| M16×Dic29 | 2 |
| C4×#90779 | 2 |
| #14270924 | 2 |
| #14270923 | 2 |
| #14270922 | 2 |
| C29×#339 | 2 |
| #1986 | 29 |