Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
310 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 66 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. #14272242 | C2 | semidirect |
| 2. #14272161 | C2 | semidirect |
| 3. #14272153 | C2 | semidirect |
| 4. #14272137 | C2 | semidirect |
| 5. #14272046 | C2 | semidirect |
| 6. #14272038 | C2 | semidirect |
| 19. C29×AGL(1,ℤ/8) | C4 | semidirect |
| 20. #11745313 | C4 | semidirect |
| 21. #11745294 | C4 | semidirect |
| 26. #11745271 | C4 | semidirect |
| 160. AGL(1,ℤ/8) | #1181 | semidirect |
| 178. C29 | #1881 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272242 | 2 |
| #14272161 | 2 |
| #14272153 | 2 |
| #14272137 | 2 |
| #14272046 | 2 |
| #14272038 | 2 |
| #14271959 | 2 |
| #1881 | 29 |