Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 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. C2×#11745312 | C2 | semidirect |
| 2. #14271730 | C2 | semidirect |
| 3. #14271646 | C2 | semidirect |
| 4. #14271383 | C2 | semidirect |
| 5. #14271376 | C2 | semidirect |
| 6. #14271361 | C2 | semidirect |
| 7. #14271356 | C2 | semidirect |
| 8. #14271191 | C2 | semidirect |
| 9. #14271165 | C2 | semidirect |
| 10. C2×#11745180 | C2 | semidirect |
| 11. C2×C29×AGL(1,ℤ/8) | C2 | semidirect |
| 21. Q8×Dic29 | C22 | semidirect |
| 22. C2×#90785 | C22 | semidirect |
| 23. C2×#90784 | C22 | semidirect |
| 29. D4×Dic29 | C22 | semidirect |
| 30. C2×#90783 | C22 | semidirect |
| 31. C2×#90782 | C22 | semidirect |
| 39. #11745169 | C22 | semidirect |
| 40. #11745164 | C22 | semidirect |
| 41. #11745162 | C22 | semidirect |
| 42. #11745162 | C22 | semidirect |
| 45. #41×C29 | D4 | semidirect |
| 148. C2×AGL(1,ℤ/8) | D29 | semidirect |
| 197. C29 | #3045 | semidirect |
| 202. #41 | C22⋊D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745312 | 2 |
| #14271730 | 2 |
| #14271646 | 2 |
| #14271383 | 2 |
| #14271376 | 2 |
| #14271361 | 2 |
| #14271356 | 2 |
| #14271191 | 2 |
| #14271165 | 2 |
| C2×#11745180 | 2 |
| C2×C29×AGL(1,ℤ/8) | 2 |
| #3045 | 29 |