Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
656 conjugacy classes of subgroups; only the 322 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 322 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. C4×#90800 | C2 | direct (N × H) |
| 3. C2×#11745218 | C2 | semidirect |
| 4. C2×C4×#6599 | C2 | semidirect |
| 9. C2×#90800 | C4 | direct (N × H) |
| 18. #11745218 | C22 | semidirect |
| 19. C4×#6599 | C22 | semidirect |
| 34. #90800 | C2×C4 | direct (N × H) |
| 35. C2×#6599 | C2×C4 | semidirect |
| 50. C2×C4×C29 | M16 | semidirect |
| 57. C2×Dic29 | M16 | semidirect |
| 65. #6599 | C22×C4 | semidirect |
| 76. C4×C29 | C2×M16 | semidirect |
| 80. Dic29 | C2×M16 | semidirect |
| 88. C2×C29 | C4×M16 | semidirect |
| 106. C29 | C2×C4×M16 | semidirect |
| 149. C2×C4 | #90800 | direct (N × H) |
| 167. C4 | C2×#90800 | direct (N × H) |
| 169. C2 | C4×#90800 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90800 | 2 |
| C4×#90800 | 2 |
| C2×#11745218 | 2 |
| C2×C4×#6599 | 2 |
| C22×C4×Dic29 | 2 |
| C2×C4×M16 | 29 |