Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
752 conjugacy classes of subgroups; only the 357 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 357 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. C4×#90779 | C2 | semidirect |
| 5. #14271009 | C2 | semidirect |
| 6. C42×Dic29 | C2 | semidirect |
| 7. C43×C29 | C2 | semidirect |
| 19. #11745234 | C4 | direct (N × H) |
| 20. C42×D29 | C4 | semidirect |
| 35. C42×C29 | C2×C4 | semidirect |
| 37. #90779 | C2×C4 | semidirect |
| 41. C4×Dic29 | C2×C4 | semidirect |
| 59. C4×D29 | C42 | semidirect |
| 69. C4×C29 | #117 | semidirect |
| 79. C43 | D29 | semidirect |
| 98. C29 | C4×#117 | semidirect |
| 118. C42 | C4×D29 | semidirect |
| 148. C4 | #11745234 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745234 | 2 |
| C2×C42×D29 | 2 |
| C4×#90779 | 2 |
| C4×#90781 | 2 |
| #14271009 | 2 |
| C42×Dic29 | 2 |
| C43×C29 | 2 |
| C4×#117 | 29 |