Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
488 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 121 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. #14271714 | C2 | semidirect |
| 2. C4×D4×D29 | C2 | semidirect |
| 3. #14271483 | C2 | semidirect |
| 4. #14271450 | C2 | semidirect |
| 5. #14271359 | C2 | semidirect |
| 6. #14271358 | C2 | semidirect |
| 7. #14271298 | C2 | semidirect |
| 8. #14271274 | C2 | semidirect |
| 9. #14271272 | C2 | semidirect |
| 10. #14271219 | C2 | semidirect |
| 11. C29×#476 | C2 | semidirect |
| 15. C29×C4⋊Q8 | C22 | semidirect |
| 26. #11745255 | C22 | semidirect |
| 30. #11745236 | C22 | semidirect |
| 33. C29×#106 | C22 | semidirect |
| 34. C29×C4⋊C8 | C22 | semidirect |
| 36. #11745169 | C22 | semidirect |
| 38. #11745163 | C22 | semidirect |
| 40. #11745157 | C22 | semidirect |
| 41. #11745156 | C22 | semidirect |
| 42. C4⋊#6597 | C22 | semidirect |
| 93. D4×C29 | #41 | semidirect |
| 112. D116 | #41 | semidirect |
| 152. #476 | D29 | semidirect |
| 171. C4⋊Q8 | C2×D29 | semidirect |
| 188. #106 | C2×D29 | semidirect |
| 190. C4⋊C8 | C2×D29 | semidirect |
| 197. C29 | #3109 | semidirect |
| 256. D4 | #90809 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271714 | 2 |
| C4×D4×D29 | 2 |
| #14271483 | 2 |
| #14271450 | 2 |
| #14271359 | 2 |
| #14271358 | 2 |
| #14271298 | 2 |
| #14271274 | 2 |
| #14271272 | 2 |
| #14271219 | 2 |
| C29×#476 | 2 |
| #3109 | 29 |