Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
1968 conjugacy classes of subgroups; only the 645 normal subgroups are shown.
This group has 1968 conjugacy classes of subgroups — too many to draw. Only its 645 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. C2×#11745291 | C2 | direct (N × H) |
| 3. C22×#90779 | C2 | semidirect |
| 4. C22×C22⋊Dic29 | C2 | semidirect |
| 5. C22×#90781 | C2 | semidirect |
| 6. C24×C4×C29 | C2 | semidirect |
| 11. C23×C4×C29 | C22 | semidirect |
| 16. C2×C22⋊Dic29 | C22 | semidirect |
| 17. #11745291 | C22 | direct (N × H) |
| 18. C2×#90781 | C22 | semidirect |
| 19. C2×#90779 | C22 | semidirect |
| 30. C22×C4×C29 | C23 | semidirect |
| 37. C22⋊Dic29 | C23 | semidirect |
| 38. #90781 | C23 | semidirect |
| 39. #90779 | C23 | semidirect |
| 62. C22×C29 | #123 | semidirect |
| 74. C24×C4 | D29 | semidirect |
| 80. C2×C29 | C2×#123 | semidirect |
| 92. C23×C4 | C2×D29 | semidirect |
| 97. C29 | C22×#123 | semidirect |
| 114. C22×C4 | C22×D29 | semidirect |
| 142. C22 | #11745291 | direct (N × H) |
| 152. C2 | C2×#11745291 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C22⋊D29 | 2 |
| C2×#11745291 | 2 |
| C22×#90779 | 2 |
| C22×C22⋊Dic29 | 2 |
| C22×#90781 | 2 |
| C24×C4×C29 | 2 |
| C22×#123 | 29 |