Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
588 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 588 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. #14271180 | C2 | semidirect |
| 3. #14271169 | C2 | semidirect |
| 4. #14271167 | C2 | semidirect |
| 5. #14271145 | C2 | semidirect |
| 6. #14271136 | C2 | semidirect |
| 7. C29×#421 | C2 | semidirect |
| 13. C2×#90809 | C4 | semidirect |
| 15. C2×D4×D29 | C4 | semidirect |
| 20. C2×M16×C29 | C22 | semidirect |
| 21. C29×#117 | C22 | semidirect |
| 22. #11745288 | C22 | semidirect |
| 23. C2×#90777 | C22 | semidirect |
| 149. #421 | D29 | semidirect |
| 174. C2×M16 | C2×D29 | semidirect |
| 176. #117 | C2×D29 | semidirect |
| 184. C29 | #1795 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745364 | 2 |
| #14271180 | 2 |
| #14271169 | 2 |
| #14271167 | 2 |
| #14271145 | 2 |
| #14271136 | 2 |
| C29×#421 | 2 |
| #1795 | 29 |