Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
738 conjugacy classes of subgroups; only the 289 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 289 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. #14271930 | C2 | semidirect |
| 2. #41×Dic29 | C2 | semidirect |
| 3. #14271180 | C2 | semidirect |
| 4. C2×#11745185 | C2 | semidirect |
| 7. C29×2−1+4 | C4 | semidirect |
| 9. C29×H(5,𝔽2) | C4 | semidirect |
| 16. #11745288 | C22 | semidirect |
| 17. C2×C4×Dic29 | C22 | semidirect |
| 18. C2×#90777 | C22 | semidirect |
| 19. #11745185 | C22 | semidirect |
| 20. #11745185 | C22 | semidirect |
| 26. #41×C29 | C2×C4 | semidirect |
| 30. C2×Q8×C29 | C2×C4 | semidirect |
| 34. C2×D4×C29 | C2×C4 | semidirect |
| 90. 2−1+4 | Dic29 | semidirect |
| 92. H(5,𝔽2) | Dic29 | semidirect |
| 104. C29 | #2901 | semidirect |
| 110. #41 | C2×Dic29 | semidirect |
| 114. C2×Q8 | C2×Dic29 | semidirect |
| 118. C2×D4 | C2×Dic29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271930 | 2 |
| #41×Dic29 | 2 |
| #14271180 | 2 |
| C2×#11745185 | 2 |
| C29×#585 | 2 |
| #2901 | 29 |