Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
544 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 157 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. C2×#11745306 | C2 | semidirect |
| 5. #14271367 | C2 | direct (N × H) |
| 6. C2×#11745162 | C2 | semidirect |
| 7. C2×#11745158 | C2 | semidirect |
| 8. C2×C29×#103 | C2 | semidirect |
| 16. #11745306 | C22 | semidirect |
| 28. C29×#103 | C22 | semidirect |
| 29. #11745162 | C22 | semidirect |
| 30. #11745158 | C22 | semidirect |
| 84. C2×Dic29 | SD16 | semidirect |
| 112. Dic29 | C2×SD16 | semidirect |
| 120. C2×#103 | D29 | semidirect |
| 121. C2×C29 | #461 | semidirect |
| 147. #103 | C2×D29 | semidirect |
| 148. C29 | C2×#461 | semidirect |
| 231. C2 | #14271367 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90773 | 2 |
| C22×#90784 | 2 |
| C2×#11745306 | 2 |
| C2×#11745255 | 2 |
| #14271367 | 2 |
| C2×#11745162 | 2 |
| C2×#11745158 | 2 |
| C2×C29×#103 | 2 |
| C2×#461 | 29 |