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×#11745311 | C2 | semidirect |
| 2. C2×#11745310 | C2 | semidirect |
| 3. #14271727 | C2 | semidirect |
| 4. #14271414 | C2 | semidirect |
| 5. #14271411 | C2 | semidirect |
| 6. #14271397 | C2 | semidirect |
| 7. #14271394 | C2 | semidirect |
| 8. #14271203 | C2 | semidirect |
| 9. #14271159 | C2 | semidirect |
| 10. C2×#11745157 | C2 | semidirect |
| 11. C29×#537 | C2 | semidirect |
| 16. C29×C22⋊Q8 | C22 | semidirect |
| 19. C29×#121 | C22 | semidirect |
| 32. C2×#90777 | C22 | semidirect |
| 34. C22×#6597 | C22 | semidirect |
| 35. #11745183 | C22 | semidirect |
| 36. #11745183 | C22 | semidirect |
| 37. #11745180 | C22 | semidirect |
| 38. #11745180 | C22 | semidirect |
| 41. #11745156 | C22 | semidirect |
| 42. #11745155 | C22 | semidirect |
| 79. #90777 | D4 | semidirect |
| 147. #537 | D29 | semidirect |
| 177. C22⋊Q8 | C2×D29 | semidirect |
| 182. #121 | C2×D29 | semidirect |
| 194. C29 | #3062 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745311 | 2 |
| C2×#11745310 | 2 |
| #14271727 | 2 |
| #14271414 | 2 |
| #14271411 | 2 |
| #14271397 | 2 |
| #14271394 | 2 |
| #14271203 | 2 |
| #14271159 | 2 |
| C2×#11745157 | 2 |
| C29×#537 | 2 |
| #3062 | 29 |