Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
1880 conjugacy classes of subgroups; only the 605 normal subgroups are shown.
This group has 1880 conjugacy classes of subgroups — too many to draw. Only its 605 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. C23×Dic58 | C2 | semidirect |
| 3. C2×#11745247 | C2 | direct (N × H) |
| 4. C22×C22⋊Dic29 | C2 | semidirect |
| 5. C22×#90781 | C2 | semidirect |
| 6. C22×#90781 | C2 | semidirect |
| 7. C22×C4×Dic29 | C2 | semidirect |
| 8. C22×C22⋊C4×C29 | C2 | semidirect |
| 19. C22×Dic58 | C22 | semidirect |
| 20. C2×C22⋊C4×C29 | C22 | semidirect |
| 21. C2×C22⋊Dic29 | C22 | semidirect |
| 22. C2×#90781 | C22 | semidirect |
| 23. C2×#90781 | C22 | semidirect |
| 24. C2×C4×Dic29 | C22 | semidirect |
| 25. #11745247 | C22 | direct (N × H) |
| 48. C2×Dic58 | C23 | semidirect |
| 49. C22⋊C4×C29 | C23 | semidirect |
| 50. C22⋊Dic29 | C23 | semidirect |
| 51. #90781 | C23 | semidirect |
| 52. #90781 | C23 | semidirect |
| 53. C4×Dic29 | C23 | semidirect |
| 85. C22×C29 | #124 | semidirect |
| 105. C22×C22⋊C4 | D29 | semidirect |
| 108. C2×C29 | C2×#124 | semidirect |
| 128. C2×C22⋊C4 | C2×D29 | semidirect |
| 130. C29 | C22×#124 | semidirect |
| 157. C22⋊C4 | C22×D29 | semidirect |
| 193. C22 | #11745247 | direct (N × H) |
| 205. C2 | C2×#11745247 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic58 | 2 |
| C23×C22⋊D29 | 2 |
| C2×#11745247 | 2 |
| C22×C22⋊Dic29 | 2 |
| C22×#90781 | 2 |
| C22×C4×Dic29 | 2 |
| C22×C22⋊C4×C29 | 2 |
| C22×#124 | 29 |