Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
548 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 131 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×#11745273 | C2 | semidirect |
| 2. #14271711 | C2 | semidirect |
| 3. C4×D4×D29 | C2 | semidirect |
| 4. #14271377 | C2 | semidirect |
| 5. #14271376 | C2 | semidirect |
| 6. #14271369 | C2 | semidirect |
| 7. #14271368 | C2 | semidirect |
| 8. #14271355 | C2 | semidirect |
| 9. #14271185 | C2 | semidirect |
| 10. #14271161 | C2 | semidirect |
| 11. C29×#459 | C2 | semidirect |
| 16. C29×#127 | C22 | semidirect |
| 20. #11745298 | C22 | semidirect |
| 36. #11745231 | C22 | semidirect |
| 37. C29×C4⋊C8 | C22 | semidirect |
| 38. C29×#102 | C22 | semidirect |
| 39. #11745180 | C22 | semidirect |
| 40. #11745164 | C22 | semidirect |
| 41. #11745162 | C22 | semidirect |
| 42. #11745158 | C22 | semidirect |
| 43. C4⋊#6597 | C22 | semidirect |
| 57. D4×D29 | D4 | semidirect |
| 146. C4×C29 | AGL(1,ℤ/8) | semidirect |
| 162. #459 | D29 | semidirect |
| 182. #127 | C2×D29 | semidirect |
| 199. C4⋊C8 | C2×D29 | semidirect |
| 203. #102 | C2×D29 | semidirect |
| 204. C29 | #3036 | semidirect |
| 311. C4 | #11745273 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745273 | 2 |
| #14271711 | 2 |
| C4×D4×D29 | 2 |
| #14271377 | 2 |
| #14271376 | 2 |
| #14271369 | 2 |
| #14271368 | 2 |
| #14271355 | 2 |
| #14271185 | 2 |
| #14271161 | 2 |
| C29×#459 | 2 |
| #3036 | 29 |