Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
500 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 133 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×#11745304 | C2 | semidirect |
| 3. C2×#11745309 | C2 | semidirect |
| 4. #14271631 | C2 | semidirect |
| 5. #14271388 | C2 | semidirect |
| 6. #14271381 | C2 | semidirect |
| 7. #14271186 | C2 | semidirect |
| 8. #14271167 | C2 | semidirect |
| 9. C29×#419 | C2 | semidirect |
| 18. C2×#90785 | C22 | semidirect |
| 20. C2×#90784 | C22 | semidirect |
| 27. #11745255 | C22 | semidirect |
| 28. #11745249 | C22 | semidirect |
| 32. C29×#103 | C22 | semidirect |
| 33. #11745162 | C22 | semidirect |
| 128. #419 | D29 | semidirect |
| 158. #103 | C2×D29 | semidirect |
| 160. C29 | #3040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745304 | 2 |
| C2×#11745270 | 2 |
| C2×#11745309 | 2 |
| #14271631 | 2 |
| #14271388 | 2 |
| #14271381 | 2 |
| #14271186 | 2 |
| #14271167 | 2 |
| C29×#419 | 2 |
| #3040 | 29 |