Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
350 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 117 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. #14271883 | C2 | semidirect |
| 2. #14271870 | C2 | semidirect |
| 3. #14271516 | C2 | semidirect |
| 4. #14271514 | C2 | semidirect |
| 5. #14271469 | C2 | semidirect |
| 6. #14271453 | C2 | semidirect |
| 8. #14271368 | C2 | semidirect |
| 9. C8×Dic58 | C2 | semidirect |
| 10. #14271254 | C2 | semidirect |
| 161. C29 | #3360 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271883 | 2 |
| #14271870 | 2 |
| #14271516 | 2 |
| #14271514 | 2 |
| #14271469 | 2 |
| #14271453 | 2 |
| #14271376 | 2 |
| #14271368 | 2 |
| C8×Dic58 | 2 |
| #14271254 | 2 |
| C4×D8×C29 | 2 |
| #3360 | 29 |