Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
548 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 143 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×#11745294 | C2 | semidirect |
| 2. #14271709 | C2 | semidirect |
| 3. C2×D4×Dic29 | C2 | semidirect |
| 4. #14271380 | C2 | semidirect |
| 5. #14271376 | C2 | semidirect |
| 6. #14271366 | C2 | semidirect |
| 7. #14271356 | C2 | semidirect |
| 8. #14271186 | C2 | semidirect |
| 9. #14271165 | C2 | semidirect |
| 10. #14271164 | C2 | semidirect |
| 11. C2×C29×AGL(1,ℤ/8) | C2 | semidirect |
| 21. #11745309 | C22 | semidirect |
| 22. #11745306 | C22 | semidirect |
| 23. #11745302 | C22 | semidirect |
| 26. #11745298 | C22 | semidirect |
| 39. #11745183 | C22 | semidirect |
| 40. #11745180 | C22 | semidirect |
| 41. #11745169 | C22 | semidirect |
| 42. #11745164 | C22 | semidirect |
| 43. #11745162 | C22 | semidirect |
| 44. #11745162 | C22 | semidirect |
| 52. C2×D4×C29 | D4 | semidirect |
| 159. Dic29 | AGL(1,ℤ/8) | semidirect |
| 161. C2×AGL(1,ℤ/8) | D29 | semidirect |
| 211. C29 | #3036 | semidirect |
| 226. C2×D4 | C22⋊D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745294 | 2 |
| #14271709 | 2 |
| C2×D4×Dic29 | 2 |
| #14271380 | 2 |
| #14271376 | 2 |
| #14271366 | 2 |
| #14271356 | 2 |
| #14271186 | 2 |
| #14271165 | 2 |
| #14271164 | 2 |
| C2×C29×AGL(1,ℤ/8) | 2 |
| #3036 | 29 |