Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
1968 conjugacy classes of subgroups; only the 605 normal subgroups are shown.
This group has 1968 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 |
|---|---|---|
| 2. C23×C4×D29 | C2 | semidirect |
| 3. C2×#11745256 | C2 | direct (N × H) |
| 4. C22×#90779 | C2 | semidirect |
| 5. C22×#90781 | C2 | semidirect |
| 6. C22×#90781 | C2 | semidirect |
| 7. C22×#90781 | C2 | semidirect |
| 8. C22×C4⋊C4×C29 | C2 | semidirect |
| 19. C22×C4×D29 | C22 | semidirect |
| 20. C2×C4⋊C4×C29 | C22 | semidirect |
| 21. C2×#90781 | C22 | semidirect |
| 22. C2×#90781 | C22 | semidirect |
| 23. C2×#90781 | C22 | semidirect |
| 24. C2×#90779 | C22 | semidirect |
| 25. #11745256 | C22 | direct (N × H) |
| 48. C2×C4×D29 | C23 | semidirect |
| 49. C4⋊C4×C29 | C23 | semidirect |
| 50. #90781 | C23 | semidirect |
| 51. #90781 | C23 | semidirect |
| 52. #90781 | C23 | semidirect |
| 53. #90779 | C23 | semidirect |
| 81. C22×C29 | #123 | semidirect |
| 103. C22×C4⋊C4 | D29 | semidirect |
| 107. C2×C29 | C2×#123 | semidirect |
| 126. C2×C4⋊C4 | C2×D29 | semidirect |
| 130. C29 | C22×#123 | semidirect |
| 155. C4⋊C4 | C22×D29 | semidirect |
| 193. C22 | #11745256 | direct (N × H) |
| 205. C2 | C2×#11745256 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D116 | 2 |
| C23×C4×D29 | 2 |
| C2×#11745256 | 2 |
| C22×#90779 | 2 |
| C22×#90781 | 2 |
| C22×C4⋊C4×C29 | 2 |
| C22×#123 | 29 |