Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
216 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 71 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. #14271211 | C2 | semidirect |
| 4. M16×Dic29 | C2 | semidirect |
| 5. #14270933 | C2 | semidirect |
| 6. #14270922 | C2 | semidirect |
| 18. #11745184 | C4 | semidirect |
| 19. #11745181 | C4 | semidirect |
| 118. C29 | #1932 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271211 | 2 |
| C2×#11745185 | 2 |
| #14271147 | 2 |
| M16×Dic29 | 2 |
| #14270933 | 2 |
| #14270922 | 2 |
| C29×#421 | 2 |
| #1932 | 29 |