Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
4632 conjugacy classes of subgroups; only the 1413 normal subgroups are shown.
This group has 4632 conjugacy classes of subgroups — too many to draw. Only its 1413 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. C24×Dic29 | C2 | semidirect |
| 3. C22×#90781 | C2 | direct (N × H) |
| 4. C24×C4×C29 | C2 | semidirect |
| 8. C24×D29 | C4 | semidirect |
| 11. C23×C4×C29 | C22 | semidirect |
| 13. C23×Dic29 | C22 | semidirect |
| 14. C2×#90781 | C22 | direct (N × H) |
| 22. C23×D29 | C2×C4 | semidirect |
| 25. C22×C4×C29 | C23 | semidirect |
| 27. C22×Dic29 | C23 | semidirect |
| 28. #90781 | C23 | direct (N × H) |
| 29. C23×C29 | C22⋊C4 | semidirect |
| 37. C22×D29 | C22×C4 | semidirect |
| 40. C2×C4×C29 | C24 | semidirect |
| 42. C2×Dic29 | C24 | semidirect |
| 44. C22×C29 | C2×C22⋊C4 | semidirect |
| 52. C2×D29 | C23×C4 | semidirect |
| 57. C24×C4 | D29 | semidirect |
| 59. C2×C29 | C22×C22⋊C4 | semidirect |
| 72. C23×C4 | C2×D29 | semidirect |
| 74. C29 | C23×C22⋊C4 | semidirect |
| 87. C22×C4 | C22×D29 | semidirect |
| 94. C23 | #90781 | direct (N × H) |
| 102. C2×C4 | C23×D29 | semidirect |
| 107. C22 | C2×#90781 | direct (N × H) |
| 115. C2 | C22×#90781 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×D29 | 2 |
| C24×Dic29 | 2 |
| C22×#90781 | 2 |
| C24×C4×C29 | 2 |
| C23×C22⋊C4 | 29 |