Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
398 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 141 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. #14271791 | C2 | semidirect |
| 3. #14271464 | C2 | semidirect |
| 4. #14271464 | C2 | semidirect |
| 5. #14271454 | C2 | semidirect |
| 6. #14271444 | C2 | semidirect |
| 7. #14271205 | C2 | semidirect |
| 8. #14271201 | C2 | semidirect |
| 11. C29×#424 | C2 | semidirect |
| 27. #11745232 | C22 | semidirect |
| 28. #11745231 | C22 | semidirect |
| 29. C29×C4⋊C8 | C22 | semidirect |
| 30. C29×C4⋊C8 | C22 | semidirect |
| 35. #11745166 | C22 | semidirect |
| 36. #11745166 | C22 | semidirect |
| 37. #11745166 | C22 | semidirect |
| 38. #11745165 | C22 | semidirect |
| 39. #11745165 | C22 | semidirect |
| 40. #11745165 | C22 | semidirect |
| 46. C2×D116 | Q8 | semidirect |
| 128. #424 | D29 | semidirect |
| 159. C4⋊C8 | C2×D29 | semidirect |
| 160. C4⋊C8 | C2×D29 | semidirect |
| 165. C29 | #3081 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271791 | 2 |
| #14271637 | 2 |
| #14271464 | 2 |
| #14271454 | 2 |
| #14271444 | 2 |
| #14271205 | 2 |
| #14271201 | 2 |
| #14271169 | 2 |
| C2×#11745169 | 2 |
| C29×#424 | 2 |
| #3081 | 29 |