Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
400 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 117 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×#11745274 | C2 | semidirect |
| 2. C2×D8×D29 | C2 | semidirect |
| 3. #14271597 | C2 | direct (N × H) |
| 4. C2×#11745148 | C2 | semidirect |
| 5. C2×#11745175 | C2 | semidirect |
| 6. C2×#11745174 | C2 | semidirect |
| 7. C2×#11745146 | C2 | semidirect |
| 8. C2×C29×D16 | C2 | semidirect |
| 12. C2×D8×C29 | C22 | semidirect |
| 16. #11745274 | C22 | semidirect |
| 18. D8×D29 | C22 | semidirect |
| 19. C2×Dic116 | C22 | semidirect |
| 22. C29×D16 | C22 | semidirect |
| 23. C2×C16×C29 | C22 | semidirect |
| 24. #11745175 | C22 | semidirect |
| 25. #11745174 | C22 | semidirect |
| 26. C2×#90768 | C22 | semidirect |
| 27. #11745148 | C22 | semidirect |
| 28. #11745146 | C22 | semidirect |
| 45. D8×C29 | C23 | semidirect |
| 51. Dic116 | C23 | semidirect |
| 56. C16×C29 | C23 | semidirect |
| 57. #90768 | C23 | semidirect |
| 104. C2×D16 | D29 | semidirect |
| 108. C2×C29 | #509 | semidirect |
| 123. C2×D8 | C2×D29 | semidirect |
| 128. D16 | C2×D29 | semidirect |
| 131. C2×C16 | C2×D29 | semidirect |
| 132. C29 | C2×#509 | semidirect |
| 155. D8 | C22×D29 | semidirect |
| 161. C16 | C22×D29 | semidirect |
| 205. C2 | #14271597 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745274 | 2 |
| C2×D8×D29 | 2 |
| #14271597 | 2 |
| C2×#11745148 | 2 |
| C2×#11745175 | 2 |
| C2×#11745174 | 2 |
| C2×#11745146 | 2 |
| C2×C29×D16 | 2 |
| C2×#509 | 29 |