Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
758 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 758 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. C22×#90807 | C2 | semidirect |
| 2. C2×#11745313 | C2 | semidirect |
| 3. #14271670 | C2 | semidirect |
| 4. #14271322 | C2 | semidirect |
| 5. #14271305 | C2 | semidirect |
| 6. #14271173 | C2 | semidirect |
| 7. #14271168 | C2 | semidirect |
| 8. #14271126 | C2 | semidirect |
| 9. C2×C29×AGL(1,ℤ/8) | C2 | semidirect |
| 21. C2×SD16×C29 | C22 | semidirect |
| 22. C2×D8×C29 | C22 | semidirect |
| 25. #11745308 | C22 | semidirect |
| 26. C2×#90785 | C22 | semidirect |
| 27. #11745300 | C22 | semidirect |
| 30. C2×#90783 | C22 | semidirect |
| 34. #11745180 | C22 | semidirect |
| 35. #11745168 | C22 | semidirect |
| 36. #11745164 | C22 | semidirect |
| 45. C2×D4×C29 | D4 | semidirect |
| 66. C2×Dic58 | D4 | semidirect |
| 142. C2×AGL(1,ℤ/8) | D29 | semidirect |
| 169. C2×SD16 | C2×D29 | semidirect |
| 170. C2×D8 | C2×D29 | semidirect |
| 182. C29 | #3005 | semidirect |
| 201. C2×D4 | C22⋊D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90807 | 2 |
| C2×#11745313 | 2 |
| #14271670 | 2 |
| #14271322 | 2 |
| #14271305 | 2 |
| #14271173 | 2 |
| #14271168 | 2 |
| #14271126 | 2 |
| C2×C29×AGL(1,ℤ/8) | 2 |
| #3005 | 29 |