Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
448 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 129 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. #14271715 | C2 | semidirect |
| 3. #14271494 | C2 | semidirect |
| 4. #14271491 | C2 | semidirect |
| 5. #14271451 | C2 | semidirect |
| 6. #14271366 | C2 | semidirect |
| 8. #14271254 | C2 | semidirect |
| 9. SD16×Dic29 | C2 | semidirect |
| 10. #14271213 | C2 | semidirect |
| 17. Q8×Dic29 | C22 | semidirect |
| 18. #11745306 | C22 | semidirect |
| 28. #11745250 | C22 | semidirect |
| 30. #11745249 | C22 | semidirect |
| 35. #11745183 | C22 | semidirect |
| 38. #11745165 | C22 | semidirect |
| 39. #11745164 | C22 | semidirect |
| 40. #11745162 | C22 | semidirect |
| 41. C8×Dic29 | C22 | semidirect |
| 42. #11745156 | C22 | semidirect |
| 103. C2×Dic29 | SD16 | semidirect |
| 179. C29 | #3101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271715 | 2 |
| C2×D4×Dic29 | 2 |
| #14271494 | 2 |
| #14271491 | 2 |
| #14271451 | 2 |
| #14271366 | 2 |
| #14271314 | 2 |
| #14271254 | 2 |
| SD16×Dic29 | 2 |
| #14271213 | 2 |
| C29×#450 | 2 |
| #3101 | 29 |