Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
548 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 2. #14271179 | C2 | semidirect |
| 3. #14271159 | C2 | semidirect |
| 4. #14271157 | C2 | semidirect |
| 5. #14271136 | C2 | semidirect |
| 6. #14271131 | C2 | semidirect |
| 7. C29×#421 | C2 | semidirect |
| 10. #11745365 | C4 | semidirect |
| 12. #11745364 | C4 | semidirect |
| 21. C2×M16×C29 | C22 | semidirect |
| 22. C29×#117 | C22 | semidirect |
| 23. #11745288 | C22 | semidirect |
| 24. C22×#6597 | C22 | semidirect |
| 162. #421 | D29 | semidirect |
| 187. C2×M16 | C2×D29 | semidirect |
| 190. #117 | C2×D29 | semidirect |
| 199. C29 | #1794 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271999 | 2 |
| #14271179 | 2 |
| #14271159 | 2 |
| #14271157 | 2 |
| #14271136 | 2 |
| #14271131 | 2 |
| C29×#421 | 2 |
| #1794 | 29 |