Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
400 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 1. C2×#11745266 | C2 | semidirect |
| 2. C22×D232 | C2 | semidirect |
| 3. #14271601 | C2 | direct (N × H) |
| 4. C2×#11745148 | C2 | semidirect |
| 5. C2×D464 | C2 | semidirect |
| 6. C2×C29×M32 | C2 | semidirect |
| 10. C2×Dic116 | C22 | semidirect |
| 12. #11745266 | C22 | semidirect |
| 16. C2×D232 | C22 | semidirect |
| 17. C2×D232 | C22 | semidirect |
| 19. C29×M32 | C22 | semidirect |
| 20. C2×C16×C29 | C22 | semidirect |
| 21. #11745148 | C22 | semidirect |
| 22. D464 | C22 | semidirect |
| 40. Dic116 | C23 | semidirect |
| 45. D232 | C23 | semidirect |
| 47. C16×C29 | C23 | semidirect |
| 88. C2×M32 | D29 | semidirect |
| 90. C2×C29 | #509 | semidirect |
| 108. M32 | C2×D29 | semidirect |
| 109. C2×C16 | C2×D29 | semidirect |
| 110. C29 | C2×#509 | semidirect |
| 135. C16 | C22×D29 | semidirect |
| 173. C2 | #14271601 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745266 | 2 |
| C22×D232 | 2 |
| #14271601 | 2 |
| C2×#11745148 | 2 |
| C2×D464 | 2 |
| C2×C29×M32 | 2 |
| C2×#509 | 29 |