Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
364 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 125 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. #14271720 | C2 | semidirect |
| 2. #14271573 | C2 | semidirect |
| 3. #14271558 | C2 | semidirect |
| 4. #14271533 | C2 | semidirect |
| 5. #14271522 | C2 | semidirect |
| 6. #14271419 | C2 | semidirect |
| 8. C4×#90785 | C2 | semidirect |
| 9. C4×#90783 | C2 | semidirect |
| 10. C4×#90777 | C2 | semidirect |
| 172. C29 | #3172 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271720 | 2 |
| #14271573 | 2 |
| #14271558 | 2 |
| #14271533 | 2 |
| #14271522 | 2 |
| #14271419 | 2 |
| #14271407 | 2 |
| C4×#90785 | 2 |
| C4×#90783 | 2 |
| C4×#90777 | 2 |
| C29×#529 | 2 |
| #3172 | 29 |