Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
564 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 173 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. C22×#90783 | C2 | semidirect |
| 2. C23×#6597 | C2 | semidirect |
| 3. C2×#11745286 | C2 | semidirect |
| 4. #14271390 | C2 | direct (N × H) |
| 5. C2×#11745156 | C2 | semidirect |
| 6. C2×#11745158 | C2 | semidirect |
| 7. C2×#11745180 | C2 | semidirect |
| 19. C2×#90783 | C22 | semidirect |
| 22. #11745286 | C22 | semidirect |
| 27. C22×#6597 | C22 | semidirect |
| 28. #11745180 | C22 | semidirect |
| 29. #11745158 | C22 | semidirect |
| 30. #11745156 | C22 | semidirect |
| 62. C2×#6597 | D4 | semidirect |
| 71. C23×C29 | SD16 | semidirect |
| 97. #6597 | C2×D4 | semidirect |
| 108. C22×C29 | C2×SD16 | semidirect |
| 128. C2×C29 | #465 | semidirect |
| 154. C29 | C2×#465 | semidirect |
| 195. C23 | #90783 | semidirect |
| 230. C22 | C2×#90783 | semidirect |
| 243. C2 | #14271390 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90783 | 2 |
| C23×#6597 | 2 |
| C2×#11745286 | 2 |
| #14271390 | 2 |
| C2×#11745156 | 2 |
| C2×#11745158 | 2 |
| C2×#11745180 | 2 |
| C2×C29×#121 | 2 |
| C2×#465 | 29 |