Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
362 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 362 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. #14271782 | C2 | semidirect |
| 2. #14271561 | C2 | semidirect |
| 3. #14271522 | C2 | semidirect |
| 4. #14271418 | C2 | semidirect |
| 6. #14271389 | C2 | semidirect |
| 7. #14271275 | C2 | semidirect |
| 8. #14271270 | C2 | semidirect |
| 9. SD16×Dic29 | C2 | semidirect |
| 10. #14271117 | C2 | semidirect |
| 11. C29×#495 | C2 | semidirect |
| 108. #495 | D29 | semidirect |
| 148. C29 | #3173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271782 | 2 |
| #14271561 | 2 |
| #14271522 | 2 |
| #14271418 | 2 |
| #14271413 | 2 |
| #14271389 | 2 |
| #14271275 | 2 |
| #14271270 | 2 |
| SD16×Dic29 | 2 |
| #14271117 | 2 |
| C29×#495 | 2 |
| #3173 | 29 |