Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
462 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 123 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. #14271874 | C2 | semidirect |
| 3. #14271480 | C2 | semidirect |
| 4. #14271450 | C2 | semidirect |
| 5. #14271391 | C2 | semidirect |
| 6. #14271360 | C2 | semidirect |
| 7. #14271315 | C2 | semidirect |
| 8. C4×#90773 | C2 | semidirect |
| 9. C8×D116 | C2 | semidirect |
| 10. #102×D29 | C2 | semidirect |
| 11. C29×#486 | C2 | semidirect |
| 14. C29×C4⋊Q8 | C22 | semidirect |
| 20. C2×#90783 | C22 | semidirect |
| 22. C2×C8×D29 | C22 | semidirect |
| 23. #11745259 | C22 | semidirect |
| 25. C4⋊C4×D29 | C22 | semidirect |
| 29. C4×Dic58 | C22 | semidirect |
| 30. C29×#102 | C22 | semidirect |
| 31. C29×#102 | C22 | semidirect |
| 32. C4×C8×C29 | C22 | semidirect |
| 33. #11745180 | C22 | semidirect |
| 35. #11745168 | C22 | semidirect |
| 36. #11745165 | C22 | semidirect |
| 37. #11745164 | C22 | semidirect |
| 39. #11745156 | C22 | semidirect |
| 40. C4⋊#6597 | C22 | semidirect |
| 99. D116 | SD16 | semidirect |
| 133. #486 | D29 | semidirect |
| 153. C4⋊Q8 | C2×D29 | semidirect |
| 173. #102 | C2×D29 | semidirect |
| 174. #102 | C2×D29 | semidirect |
| 176. C4×C8 | C2×D29 | semidirect |
| 177. C29 | #3295 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271874 | 2 |
| #14271798 | 2 |
| #14271480 | 2 |
| #14271450 | 2 |
| #14271391 | 2 |
| #14271360 | 2 |
| #14271315 | 2 |
| C4×#90773 | 2 |
| C8×D116 | 2 |
| #102×D29 | 2 |
| C29×#486 | 2 |
| #3295 | 29 |