Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
376 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 101 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. C22×#90777 | C2 | semidirect |
| 2. C2×#11745185 | C2 | semidirect |
| 3. C4×C22⋊Dic29 | C2 | semidirect |
| 4. #14270922 | C2 | semidirect |
| 9. C29×C22⋊Q8 | C4 | semidirect |
| 10. C29×C22⋊Q8 | C4 | semidirect |
| 11. C29×#121 | C4 | semidirect |
| 12. C29×#121 | C4 | semidirect |
| 58. #90777 | D4 | semidirect |
| 107. C22×C29 | #104 | semidirect |
| 138. C22⋊Q8 | Dic29 | semidirect |
| 139. C22⋊Q8 | Dic29 | semidirect |
| 140. #121 | Dic29 | semidirect |
| 141. #121 | Dic29 | semidirect |
| 150. C29 | #1871 | semidirect |
| 232. C22 | #11745185 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90777 | 2 |
| C2×#11745185 | 2 |
| C4×C22⋊Dic29 | 2 |
| #14270922 | 2 |
| C29×#525 | 2 |
| #1871 | 29 |