Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
306 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 4. #14270924 | C2 | semidirect |
| 5. #14270923 | C2 | semidirect |
| 6. #14270922 | C2 | semidirect |
| 7. C29×#339 | C2 | semidirect |
| 16. #11745254 | C4 | semidirect |
| 17. #11745254 | C4 | semidirect |
| 18. C4⋊C4×D29 | C4 | semidirect |
| 19. C4⋊C4×D29 | C4 | semidirect |
| 138. #339 | D29 | semidirect |
| 165. C29 | #1826 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #117×D29 | 2 |
| #14271126 | 2 |
| C4×#90781 | 2 |
| #14270924 | 2 |
| #14270923 | 2 |
| #14270922 | 2 |
| C29×#339 | 2 |
| #1826 | 29 |