Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
440 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 135 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. #14271716 | C2 | semidirect |
| 3. #14271466 | C2 | semidirect |
| 4. #14271462 | C2 | semidirect |
| 5. #14271452 | C2 | semidirect |
| 6. #14271442 | C2 | semidirect |
| 7. #14271203 | C2 | semidirect |
| 8. #14271186 | C2 | semidirect |
| 11. C29×#428 | C2 | semidirect |
| 25. #11745252 | C22 | semidirect |
| 26. #11745252 | C22 | semidirect |
| 27. #11745250 | C22 | semidirect |
| 28. #11745250 | C22 | semidirect |
| 33. C29×#107 | C22 | semidirect |
| 34. C29×#106 | C22 | semidirect |
| 37. #11745162 | C22 | semidirect |
| 38. #11745162 | C22 | semidirect |
| 41. #11745156 | C22 | semidirect |
| 42. #11745155 | C22 | semidirect |
| 50. C2×D116 | Q8 | semidirect |
| 141. #428 | D29 | semidirect |
| 172. #107 | C2×D29 | semidirect |
| 174. #106 | C2×D29 | semidirect |
| 181. C29 | #3077 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271716 | 2 |
| C2×#11745255 | 2 |
| #14271466 | 2 |
| #14271462 | 2 |
| #14271452 | 2 |
| #14271442 | 2 |
| #14271203 | 2 |
| #14271186 | 2 |
| #14271169 | 2 |
| #14271167 | 2 |
| C29×#428 | 2 |
| #3077 | 29 |