Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
752 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#11745271 | C2 | semidirect |
| 3. C22×#90773 | C2 | semidirect |
| 4. #14271734 | C2 | semidirect |
| 5. #14271327 | C2 | semidirect |
| 6. #14271316 | C2 | semidirect |
| 7. #14271169 | C2 | semidirect |
| 8. #14271160 | C2 | semidirect |
| 9. C29×#408 | C2 | semidirect |
| 20. C22×Dic58 | C22 | semidirect |
| 21. C2×M16×C29 | C22 | semidirect |
| 22. C22×C8×C29 | C22 | semidirect |
| 26. #11745288 | C22 | semidirect |
| 27. #11745286 | C22 | semidirect |
| 29. C2×Dic116 | C22 | semidirect |
| 31. C2×#90773 | C22 | semidirect |
| 32. C2×#90773 | C22 | semidirect |
| 33. C29×C22⋊C8 | C22 | semidirect |
| 34. #11745169 | C22 | semidirect |
| 35. #11745169 | C22 | semidirect |
| 36. #11745164 | C22 | semidirect |
| 149. #408 | D29 | semidirect |
| 172. C2×M16 | C2×D29 | semidirect |
| 173. C22×C8 | C2×D29 | semidirect |
| 182. C22⋊C8 | C2×D29 | semidirect |
| 183. C29 | #3009 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745364 | 2 |
| C2×#11745271 | 2 |
| C22×#90773 | 2 |
| #14271734 | 2 |
| #14271327 | 2 |
| #14271316 | 2 |
| #14271169 | 2 |
| #14271160 | 2 |
| C29×#408 | 2 |
| #3009 | 29 |