Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
462 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 462 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. #14271870 | C2 | semidirect |
| 2. #14271509 | C2 | semidirect |
| 3. #14271479 | C2 | semidirect |
| 4. #14271453 | C2 | semidirect |
| 5. #14271390 | C2 | semidirect |
| 6. #14271360 | C2 | semidirect |
| 7. #14271314 | C2 | semidirect |
| 8. C4×#90783 | C2 | semidirect |
| 9. D4×#6597 | C2 | semidirect |
| 10. C2×#11745180 | C2 | semidirect |
| 22. C2×#90783 | C22 | semidirect |
| 23. C2×C4⋊Dic29 | C22 | semidirect |
| 24. #11745286 | C22 | semidirect |
| 25. C22×#6597 | C22 | semidirect |
| 28. #11745231 | C22 | semidirect |
| 29. C4×Dic58 | C22 | semidirect |
| 32. #11745180 | C22 | semidirect |
| 33. #11745180 | C22 | semidirect |
| 34. #11745180 | C22 | semidirect |
| 35. C22⋊#6597 | C22 | semidirect |
| 36. #11745158 | C22 | semidirect |
| 37. #11745156 | C22 | semidirect |
| 38. #11745156 | C22 | semidirect |
| 39. C4⋊#6597 | C22 | semidirect |
| 40. C4×#6597 | C22 | semidirect |
| 90. D4×C29 | SD16 | semidirect |
| 177. C29 | #3295 | semidirect |
| 230. D4 | #90783 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271870 | 2 |
| #14271509 | 2 |
| #14271479 | 2 |
| #14271453 | 2 |
| #14271390 | 2 |
| #14271360 | 2 |
| #14271314 | 2 |
| C4×#90783 | 2 |
| D4×#6597 | 2 |
| C2×#11745180 | 2 |
| D42×C29 | 2 |
| #3295 | 29 |