Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
360 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 113 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. #14271976 | C2 | semidirect |
| 2. #14271965 | C2 | semidirect |
| 3. #14271605 | C2 | semidirect |
| 4. #14271601 | C2 | semidirect |
| 5. #14271600 | C2 | semidirect |
| 6. #14271596 | C2 | semidirect |
| 7. #14271593 | C2 | semidirect |
| 8. C2×#11745176 | C2 | semidirect |
| 9. SD32×D29 | C2 | semidirect |
| 10. #14271581 | C2 | semidirect |
| 11. C29×#510 | C2 | semidirect |
| 15. C2×Q16×C29 | C22 | semidirect |
| 19. #11745281 | C22 | semidirect |
| 21. Q16×D29 | C22 | semidirect |
| 24. #11745266 | C22 | semidirect |
| 27. C29×Q32 | C22 | semidirect |
| 28. C29×SD32 | C22 | semidirect |
| 29. C29×M32 | C22 | semidirect |
| 30. #11745177 | C22 | semidirect |
| 31. #11745176 | C22 | semidirect |
| 32. #11745176 | C22 | semidirect |
| 33. #11745176 | C22 | semidirect |
| 34. #11745175 | C22 | semidirect |
| 35. #11745174 | C22 | semidirect |
| 36. C2×#90768 | C22 | semidirect |
| 37. #11745148 | C22 | semidirect |
| 38. D464 | C22 | semidirect |
| 39. #11745146 | C22 | semidirect |
| 40. C16×D29 | C22 | semidirect |
| 124. #510 | D29 | semidirect |
| 149. C2×Q16 | C2×D29 | semidirect |
| 154. Q32 | C2×D29 | semidirect |
| 160. SD32 | C2×D29 | semidirect |
| 164. M32 | C2×D29 | semidirect |
| 167. C29 | #3416 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271976 | 2 |
| #14271965 | 2 |
| #14271605 | 2 |
| #14271601 | 2 |
| #14271600 | 2 |
| #14271596 | 2 |
| #14271593 | 2 |
| C2×#11745176 | 2 |
| SD32×D29 | 2 |
| #14271581 | 2 |
| C29×#510 | 2 |
| #3416 | 29 |