Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 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×#11745304 | C2 | semidirect |
| 3. C4×#90805 | C2 | semidirect |
| 4. #14271382 | C2 | semidirect |
| 5. #14271375 | C2 | semidirect |
| 6. #14271187 | C2 | semidirect |
| 7. #14271172 | C2 | semidirect |
| 8. #14271168 | C2 | semidirect |
| 9. C2×C29×#124 | C2 | semidirect |
| 18. C2×#90785 | C22 | semidirect |
| 20. C2×#90784 | C22 | semidirect |
| 28. C4×D116 | C22 | semidirect |
| 31. C4×Dic58 | C22 | semidirect |
| 32. #11745183 | C22 | semidirect |
| 34. C4⋊#6597 | C22 | semidirect |
| 123. C2×#124 | 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×#11745294 | 2 |
| C4×#90805 | 2 |
| #14271382 | 2 |
| #14271375 | 2 |
| #14271187 | 2 |
| #14271172 | 2 |
| #14271168 | 2 |
| C2×C29×#124 | 2 |
| #3040 | 29 |