Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
548 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 121 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. #14271180 | C2 | semidirect |
| 2. #14271159 | C2 | semidirect |
| 3. #14271137 | C2 | semidirect |
| 4. #14271130 | C2 | semidirect |
| 7. C29×2−1+4 | C4 | semidirect |
| 10. C29×H(5,𝔽2) | C4 | semidirect |
| 15. #11745288 | C22 | semidirect |
| 16. C2×#90777 | C22 | semidirect |
| 17. C22×#6597 | C22 | semidirect |
| 115. 2−1+4 | Dic29 | semidirect |
| 118. H(5,𝔽2) | Dic29 | semidirect |
| 131. C29 | #1794 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271180 | 2 |
| #14271159 | 2 |
| #14271137 | 2 |
| #14271130 | 2 |
| C29×#585 | 2 |
| #1794 | 29 |