Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
596 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 149 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×#11745270 | C2 | semidirect |
| 2. C2×#11745312 | C2 | semidirect |
| 3. C22×#90782 | C2 | semidirect |
| 4. #14271730 | C2 | semidirect |
| 5. #14271727 | C2 | semidirect |
| 6. #14271551 | C2 | semidirect |
| 7. #14271549 | C2 | semidirect |
| 8. #14271544 | C2 | semidirect |
| 9. #14271538 | C2 | semidirect |
| 10. #14271121 | C2 | semidirect |
| 11. C2×C29×AGL(1,ℤ/8) | C2 | semidirect |
| 17. C2×SD16×C29 | C22 | semidirect |
| 18. C2×D8×C29 | C22 | semidirect |
| 22. #11745309 | C22 | semidirect |
| 23. C2×#90785 | C22 | semidirect |
| 24. C2×#90784 | C22 | semidirect |
| 25. #11745302 | C22 | semidirect |
| 26. #11745302 | C22 | semidirect |
| 29. #11745298 | C22 | semidirect |
| 30. C2×#90783 | C22 | semidirect |
| 34. C2×#90782 | C22 | semidirect |
| 39. C2×D232 | C22 | semidirect |
| 40. C2×#90773 | C22 | semidirect |
| 41. #11745163 | C22 | semidirect |
| 42. C8×Dic29 | C22 | semidirect |
| 70. M16×C29 | D4 | semidirect |
| 83. C2×#6597 | D4 | semidirect |
| 148. C2×AGL(1,ℤ/8) | D29 | semidirect |
| 176. C2×SD16 | C2×D29 | semidirect |
| 182. C2×D8 | C2×D29 | semidirect |
| 196. C29 | #3155 | semidirect |
| 232. M16 | C22⋊D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745270 | 2 |
| C2×#11745312 | 2 |
| C22×#90782 | 2 |
| #14271730 | 2 |
| #14271727 | 2 |
| #14271551 | 2 |
| #14271549 | 2 |
| #14271544 | 2 |
| #14271538 | 2 |
| #14271121 | 2 |
| C2×C29×AGL(1,ℤ/8) | 2 |
| #3155 | 29 |