Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
404 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 135 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 |
|---|---|---|
| 3. #14270920 | C2 | semidirect |
| 4. #14270919 | C2 | semidirect |
| 5. C29×H(3,ℤ/4) | C2 | semidirect |
| 13. C2×#90772 | C4 | semidirect |
| 14. C2×C8×D29 | C4 | semidirect |
| 19. #11745234 | C4 | semidirect |
| 20. C42×D29 | C4 | semidirect |
| 34. C2×C8×C29 | C2×C4 | semidirect |
| 37. C42×C29 | C2×C4 | semidirect |
| 43. C4×Dic29 | C2×C4 | semidirect |
| 45. C2×#6597 | C2×C4 | semidirect |
| 101. H(3,ℤ/4) | D29 | direct (N × H) |
| 107. D29 | H(3,ℤ/4) | direct (N × H) |
| 123. C29 | C2×H(3,ℤ/4) | semidirect |
| 142. C2×C8 | C4×D29 | semidirect |
| 151. C42 | C4×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M16×D29 | 2 |
| #117×D29 | 2 |
| #14270920 | 2 |
| #14270919 | 2 |
| C29×H(3,ℤ/4) | 2 |
| C2×H(3,ℤ/4) | 29 |