Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
400 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 125 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×Q16×D29 | C2 | semidirect |
| 3. C2×#11745148 | C2 | semidirect |
| 4. C2×#11745175 | C2 | semidirect |
| 5. C2×#11745176 | C2 | semidirect |
| 6. SD32×D29 | C2 | direct (N × H) |
| 7. C2×C16×D29 | C2 | semidirect |
| 8. C2×C29×SD32 | C2 | semidirect |
| 11. C2×Q16×C29 | C22 | semidirect |
| 16. Q16×D29 | C22 | semidirect |
| 19. C2×Dic116 | C22 | semidirect |
| 22. C29×SD32 | C22 | semidirect |
| 23. C2×C16×C29 | C22 | semidirect |
| 24. #11745176 | C22 | semidirect |
| 25. #11745175 | C22 | semidirect |
| 26. C2×#90768 | C22 | semidirect |
| 27. #11745148 | C22 | semidirect |
| 28. C16×D29 | C22 | semidirect |
| 43. Q16×C29 | C23 | semidirect |
| 51. Dic116 | C23 | semidirect |
| 56. C16×C29 | C23 | semidirect |
| 57. #90768 | C23 | semidirect |
| 90. C2×D29 | SD32 | direct (N × H) |
| 103. C2×SD32 | D29 | direct (N × H) |
| 106. C2×C29 | C2×SD32 | semidirect |
| 109. D29 | C2×SD32 | direct (N × H) |
| 116. C2×Q16 | C2×D29 | semidirect |
| 126. SD32 | C2×D29 | direct (N × H) |
| 129. C2×C16 | C2×D29 | semidirect |
| 130. C29 | C22×SD32 | semidirect |
| 148. Q16 | C22×D29 | semidirect |
| 159. C16 | C22×D29 | semidirect |
| 201. C2 | SD32×D29 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D29 | 2 |
| C2×D8×D29 | 2 |
| C2×#11745148 | 2 |
| C2×#11745175 | 2 |
| C2×#11745176 | 2 |
| SD32×D29 | 2 |
| C2×C16×D29 | 2 |
| C2×C29×SD32 | 2 |
| C22×SD32 | 29 |