Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
448 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 127 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. #14271718 | C2 | semidirect |
| 3. #14271492 | C2 | semidirect |
| 4. #14271454 | C2 | semidirect |
| 5. #14271453 | C2 | semidirect |
| 6. #14271365 | C2 | semidirect |
| 8. SD16×Dic29 | C2 | semidirect |
| 9. #14271248 | C2 | semidirect |
| 10. #14271215 | C2 | semidirect |
| 11. C29×#461 | C2 | semidirect |
| 15. C29×C4⋊Q8 | C22 | semidirect |
| 18. Q8×Dic29 | C22 | semidirect |
| 32. #11745231 | C22 | semidirect |
| 33. C29×C4⋊C8 | C22 | semidirect |
| 34. C29×#103 | C22 | semidirect |
| 35. #11745183 | C22 | semidirect |
| 39. #11745165 | C22 | semidirect |
| 40. C8×Dic29 | C22 | semidirect |
| 41. #11745156 | C22 | semidirect |
| 42. C4⋊#6597 | C22 | semidirect |
| 114. C4×D29 | SD16 | semidirect |
| 147. #461 | D29 | semidirect |
| 163. C4⋊Q8 | C2×D29 | semidirect |
| 182. C4⋊C8 | C2×D29 | semidirect |
| 184. #103 | C2×D29 | semidirect |
| 189. C29 | #3101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271718 | 2 |
| C4×D4×D29 | 2 |
| #14271492 | 2 |
| #14271454 | 2 |
| #14271453 | 2 |
| #14271365 | 2 |
| #14271312 | 2 |
| SD16×Dic29 | 2 |
| #14271248 | 2 |
| #14271215 | 2 |
| C29×#461 | 2 |
| #3101 | 29 |