Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
364 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 119 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. #14271718 | C2 | semidirect |
| 3. #14271572 | C2 | semidirect |
| 4. #14271531 | C2 | semidirect |
| 5. #14271522 | C2 | semidirect |
| 6. #14271418 | C2 | semidirect |
| 8. Q16×Dic29 | C2 | semidirect |
| 9. SD16×Dic29 | C2 | semidirect |
| 10. #14271115 | C2 | semidirect |
| 11. C29×#497 | C2 | semidirect |
| 128. #497 | D29 | semidirect |
| 172. C29 | #3172 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271718 | 2 |
| #14271692 | 2 |
| #14271572 | 2 |
| #14271531 | 2 |
| #14271522 | 2 |
| #14271418 | 2 |
| #14271406 | 2 |
| Q16×Dic29 | 2 |
| SD16×Dic29 | 2 |
| #14271115 | 2 |
| C29×#497 | 2 |
| #3172 | 29 |