Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
404 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 125 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. #14271794 | C2 | semidirect |
| 3. #14271526 | C2 | semidirect |
| 4. #14271521 | C2 | semidirect |
| 5. #14271516 | C2 | semidirect |
| 6. #14271508 | C2 | semidirect |
| 7. #14271168 | C2 | semidirect |
| 8. #14271162 | C2 | semidirect |
| 9. #14271160 | C2 | semidirect |
| 10. #14271118 | C2 | semidirect |
| 11. C2×C29×#102 | C2 | semidirect |
| 26. #11745252 | C22 | semidirect |
| 28. #11745250 | C22 | semidirect |
| 33. #11745169 | C22 | semidirect |
| 34. #11745169 | C22 | semidirect |
| 35. #11745164 | C22 | semidirect |
| 36. #11745164 | C22 | semidirect |
| 37. #11745163 | C22 | semidirect |
| 38. C8×Dic29 | C22 | semidirect |
| 39. #11745158 | C22 | semidirect |
| 40. #11745157 | C22 | semidirect |
| 139. C2×#102 | D29 | semidirect |
| 176. C29 | #3136 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271794 | 2 |
| #14271730 | 2 |
| #14271526 | 2 |
| #14271521 | 2 |
| #14271516 | 2 |
| #14271508 | 2 |
| #14271168 | 2 |
| #14271162 | 2 |
| #14271160 | 2 |
| #14271118 | 2 |
| C2×C29×#102 | 2 |
| #3136 | 29 |