Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
398 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 133 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. #14271466 | C2 | semidirect |
| 4. #14271462 | C2 | semidirect |
| 5. #14271452 | C2 | semidirect |
| 6. #14271442 | C2 | semidirect |
| 7. #14271206 | C2 | semidirect |
| 8. #14271189 | C2 | semidirect |
| 11. C29×#427 | C2 | semidirect |
| 21. #11745252 | C22 | semidirect |
| 22. #11745250 | C22 | semidirect |
| 29. C29×#107 | C22 | semidirect |
| 30. C29×#107 | C22 | semidirect |
| 31. C29×#106 | C22 | semidirect |
| 32. C29×#106 | C22 | semidirect |
| 35. #11745162 | C22 | semidirect |
| 36. #11745162 | C22 | semidirect |
| 39. #11745156 | C22 | semidirect |
| 40. #11745155 | C22 | semidirect |
| 46. C2×D116 | Q8 | semidirect |
| 127. #427 | D29 | semidirect |
| 154. #107 | C2×D29 | semidirect |
| 155. #107 | C2×D29 | semidirect |
| 157. #106 | C2×D29 | semidirect |
| 158. #106 | 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 |
| #14271466 | 2 |
| #14271462 | 2 |
| #14271452 | 2 |
| #14271442 | 2 |
| #14271206 | 2 |
| #14271189 | 2 |
| #14271167 | 2 |
| C2×#11745169 | 2 |
| C29×#427 | 2 |
| #3081 | 29 |