Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
752 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 165 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×#11745313 | C2 | semidirect |
| 2. C22×#90783 | C2 | semidirect |
| 3. #14271734 | C2 | semidirect |
| 4. #14271325 | C2 | semidirect |
| 5. #14271314 | C2 | semidirect |
| 6. #14271168 | C2 | semidirect |
| 7. #14271159 | C2 | semidirect |
| 8. #14271130 | C2 | semidirect |
| 20. C22×Dic58 | C22 | semidirect |
| 23. C2×#90785 | C22 | semidirect |
| 27. C2×#90783 | C22 | semidirect |
| 28. C2×#90783 | C22 | semidirect |
| 29. #11745288 | C22 | semidirect |
| 30. #11745286 | C22 | semidirect |
| 31. C2×#90777 | C22 | semidirect |
| 32. C22×#6597 | C22 | semidirect |
| 33. #11745183 | C22 | semidirect |
| 34. #11745180 | C22 | semidirect |
| 35. #11745180 | C22 | semidirect |
| 36. C22⋊#6597 | C22 | semidirect |
| 183. C29 | #3009 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745313 | 2 |
| C22×#90783 | 2 |
| #14271734 | 2 |
| #14271325 | 2 |
| #14271314 | 2 |
| #14271168 | 2 |
| #14271159 | 2 |
| #14271130 | 2 |
| C2×C29×H(5,𝔽2) | 2 |
| #3009 | 29 |