Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
484 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 484 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. #14271719 | C2 | semidirect |
| 3. #14271529 | C2 | semidirect |
| 4. #14271528 | C2 | semidirect |
| 5. #14271527 | C2 | semidirect |
| 6. #14271508 | C2 | semidirect |
| 7. #14271166 | C2 | semidirect |
| 8. #14271115 | C2 | semidirect |
| 9. C29×#490 | C2 | semidirect |
| 13. C29×#125 | C22 | semidirect |
| 19. #11745250 | C22 | semidirect |
| 23. #11745232 | C22 | semidirect |
| 24. C29×#102 | C22 | semidirect |
| 25. C29×#97 | C22 | semidirect |
| 26. #11745180 | C22 | semidirect |
| 27. #11745169 | C22 | semidirect |
| 28. C8×Dic29 | C22 | semidirect |
| 29. #11745157 | C22 | semidirect |
| 30. #11745151 | C22 | semidirect |
| 98. #490 | D29 | semidirect |
| 116. #125 | C2×D29 | semidirect |
| 124. #102 | C2×D29 | semidirect |
| 126. #97 | C2×D29 | semidirect |
| 128. C29 | #3138 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271719 | 2 |
| #127×D29 | 2 |
| #14271529 | 2 |
| #14271528 | 2 |
| #14271527 | 2 |
| #14271508 | 2 |
| #14271166 | 2 |
| #14271115 | 2 |
| C29×#490 | 2 |
| #3138 | 29 |