Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
756 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 756 conjugacy classes of subgroups — too many to draw. Only its 209 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. #14271929 | C2 | semidirect |
| 3. #14271147 | C2 | semidirect |
| 4. #14271146 | C2 | semidirect |
| 5. C2×#11745171 | C2 | semidirect |
| 6. #100×D29 | C2 | semidirect |
| 7. C29×#413 | C2 | semidirect |
| 18. C2×M16×C29 | C22 | semidirect |
| 19. C2×#90777 | C22 | semidirect |
| 21. M16×D29 | C22 | semidirect |
| 23. C29×#101 | C22 | semidirect |
| 24. C29×#100 | C22 | semidirect |
| 25. #11745184 | C22 | semidirect |
| 26. #11745181 | C22 | semidirect |
| 27. #11745171 | C22 | semidirect |
| 119. #413 | D29 | semidirect |
| 142. C2×M16 | C2×D29 | semidirect |
| 144. #101 | C2×D29 | semidirect |
| 147. #100 | C2×D29 | semidirect |
| 148. C29 | #2888 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745364 | 2 |
| #14271929 | 2 |
| #14271147 | 2 |
| #14271146 | 2 |
| C2×#11745171 | 2 |
| #100×D29 | 2 |
| C29×#413 | 2 |
| #2888 | 29 |