Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
360 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 2. C2×Q16×D29 | C2 | semidirect |
| 3. #14271606 | C2 | semidirect |
| 4. #14271605 | C2 | semidirect |
| 5. #14271604 | C2 | semidirect |
| 6. #14271603 | C2 | semidirect |
| 7. #14271602 | C2 | semidirect |
| 8. Q32×D29 | C2 | semidirect |
| 9. SD32×D29 | C2 | semidirect |
| 10. M32×D29 | C2 | semidirect |
| 11. C29×#510 | C2 | semidirect |
| 15. C2×Q16×C29 | C22 | semidirect |
| 23. Q16×D29 | C22 | semidirect |
| 28. C2×Dic116 | C22 | semidirect |
| 31. C29×Q32 | C22 | semidirect |
| 32. C29×SD32 | C22 | semidirect |
| 33. C29×M32 | C22 | semidirect |
| 34. #11745177 | C22 | semidirect |
| 35. #11745177 | C22 | semidirect |
| 36. #11745176 | C22 | semidirect |
| 37. #11745175 | C22 | semidirect |
| 38. #11745160 | C22 | semidirect |
| 39. Dic232 | C22 | semidirect |
| 40. #11745148 | C22 | semidirect |
| 41. #11745146 | C22 | semidirect |
| 146. #510 | D29 | direct (N × H) |
| 155. D29 | #510 | direct (N × H) |
| 171. C2×Q16 | C2×D29 | semidirect |
| 178. Q32 | C2×D29 | semidirect |
| 182. SD32 | C2×D29 | semidirect |
| 185. M32 | C2×D29 | semidirect |
| 187. C29 | C2×#510 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #135×D29 | 2 |
| C2×Q16×D29 | 2 |
| #14271606 | 2 |
| #14271605 | 2 |
| #14271604 | 2 |
| #14271603 | 2 |
| #14271602 | 2 |
| Q32×D29 | 2 |
| SD32×D29 | 2 |
| M32×D29 | 2 |
| C29×#510 | 2 |
| C2×#510 | 29 |