Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
454 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 117 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. #14271980 | C2 | semidirect |
| 2. #14271973 | C2 | semidirect |
| 3. #14271964 | C2 | semidirect |
| 4. #14271546 | C2 | semidirect |
| 5. #14271439 | C2 | semidirect |
| 6. #14271425 | C2 | semidirect |
| 7. #14271343 | C2 | semidirect |
| 8. #14271334 | C2 | semidirect |
| 9. #14271279 | C2 | semidirect |
| 10. #14271278 | C2 | semidirect |
| 11. C29×#472 | C2 | semidirect |
| 12. #11745365 | C22 | semidirect |
| 14. C29×AGL(1,ℤ/8) | C22 | semidirect |
| 16. C29×#131 | C22 | semidirect |
| 18. #11745298 | C22 | semidirect |
| 19. C2×#90783 | C22 | semidirect |
| 30. #11745271 | C22 | semidirect |
| 31. #11745269 | C22 | semidirect |
| 33. C2×Dic116 | C22 | semidirect |
| 37. C29×#108 | C22 | semidirect |
| 38. C29×#100 | C22 | semidirect |
| 39. #11745185 | C22 | semidirect |
| 41. #11745173 | C22 | semidirect |
| 42. #11745172 | C22 | semidirect |
| 43. #11745170 | C22 | semidirect |
| 44. C8×Dic29 | C22 | semidirect |
| 149. #472 | D29 | semidirect |
| 170. AGL(1,ℤ/8) | C2×D29 | semidirect |
| 184. #131 | C2×D29 | semidirect |
| 187. #108 | C2×D29 | semidirect |
| 192. #100 | C2×D29 | semidirect |
| 194. C29 | #3290 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271980 | 2 |
| #14271973 | 2 |
| #14271964 | 2 |
| #14271546 | 2 |
| #14271439 | 2 |
| #14271425 | 2 |
| #14271343 | 2 |
| #14271334 | 2 |
| #14271279 | 2 |
| #14271278 | 2 |
| C29×#472 | 2 |
| #3290 | 29 |