Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
736 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 736 conjugacy classes of subgroups — too many to draw. Only its 161 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. #14271727 | C2 | semidirect |
| 3. #14271336 | C2 | semidirect |
| 4. #14271331 | C2 | semidirect |
| 5. #14271180 | C2 | semidirect |
| 6. #14271147 | C2 | semidirect |
| 7. C29×#585 | C2 | semidirect |
| 9. C29×2−1+4 | C22 | semidirect |
| 12. C29×H(5,𝔽2) | C22 | semidirect |
| 17. C22×D116 | C22 | semidirect |
| 19. #11745311 | C22 | semidirect |
| 20. #11745309 | C22 | semidirect |
| 22. #11745302 | C22 | semidirect |
| 26. #11745288 | C22 | semidirect |
| 27. C2×#90777 | C22 | semidirect |
| 28. #11745185 | C22 | semidirect |
| 29. #11745184 | C22 | semidirect |
| 30. #11745181 | C22 | semidirect |
| 42. #41×C29 | D4 | semidirect |
| 46. C2×Q8×C29 | D4 | semidirect |
| 54. C2×D4×C29 | D4 | semidirect |
| 129. #585 | D29 | semidirect |
| 143. 2−1+4 | C2×D29 | semidirect |
| 146. H(5,𝔽2) | C2×D29 | semidirect |
| 165. C29 | #3021 | semidirect |
| 177. #41 | C22⋊D29 | semidirect |
| 181. C2×Q8 | C22⋊D29 | semidirect |
| 194. C2×D4 | C22⋊D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745311 | 2 |
| #14271727 | 2 |
| #14271336 | 2 |
| #14271331 | 2 |
| #14271180 | 2 |
| #14271147 | 2 |
| C29×#585 | 2 |
| #3021 | 29 |