Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
462 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 139 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. #14271870 | C2 | semidirect |
| 3. #14271510 | C2 | semidirect |
| 4. #14271482 | C2 | semidirect |
| 5. #14271454 | C2 | semidirect |
| 6. #14271392 | C2 | semidirect |
| 7. #14271364 | C2 | semidirect |
| 8. #14271316 | C2 | semidirect |
| 9. C4×#90773 | C2 | semidirect |
| 10. C2×#11745169 | C2 | semidirect |
| 11. C8×D4×C29 | C2 | semidirect |
| 14. C22×C8×C29 | C22 | semidirect |
| 18. C2×C4⋊Dic29 | C22 | semidirect |
| 19. #11745286 | C22 | semidirect |
| 21. C2×#90773 | C22 | semidirect |
| 28. #11745231 | C22 | semidirect |
| 29. C4×Dic58 | C22 | semidirect |
| 30. C29×C4⋊C8 | C22 | semidirect |
| 31. C29×C22⋊C8 | C22 | semidirect |
| 32. C4×C8×C29 | C22 | semidirect |
| 35. #11745169 | C22 | semidirect |
| 36. #11745169 | C22 | semidirect |
| 37. #11745169 | C22 | semidirect |
| 38. #11745165 | C22 | semidirect |
| 39. #11745165 | C22 | semidirect |
| 40. #11745164 | C22 | semidirect |
| 83. D4×C29 | SD16 | semidirect |
| 140. C8×D4 | D29 | semidirect |
| 152. C22×C8 | C2×D29 | semidirect |
| 168. C4⋊C8 | C2×D29 | semidirect |
| 175. C22⋊C8 | C2×D29 | semidirect |
| 176. C4×C8 | C2×D29 | semidirect |
| 177. C29 | #3295 | semidirect |
| 231. D4 | #90773 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271870 | 2 |
| D4×D116 | 2 |
| #14271510 | 2 |
| #14271482 | 2 |
| #14271454 | 2 |
| #14271392 | 2 |
| #14271364 | 2 |
| #14271316 | 2 |
| C4×#90773 | 2 |
| C2×#11745169 | 2 |
| C8×D4×C29 | 2 |
| #3295 | 29 |