Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
736 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 736 conjugacy classes of subgroups — too many to draw. Only its 145 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. #14271999 | C2 | semidirect |
| 2. C2×#11745270 | C2 | semidirect |
| 3. #14271727 | C2 | semidirect |
| 4. #14271338 | C2 | semidirect |
| 5. #14271333 | C2 | semidirect |
| 6. #14271179 | C2 | semidirect |
| 7. C29×#413 | C2 | semidirect |
| 12. #11745362 | C22 | semidirect |
| 14. #11745359 | C22 | semidirect |
| 17. C22×D116 | C22 | semidirect |
| 18. C2×M16×C29 | C22 | semidirect |
| 19. #11745309 | C22 | semidirect |
| 20. #11745302 | C22 | semidirect |
| 23. #11745288 | C22 | semidirect |
| 25. #11745270 | C22 | semidirect |
| 28. C29×#101 | C22 | semidirect |
| 29. C29×#100 | C22 | semidirect |
| 30. #11745173 | C22 | semidirect |
| 53. #90805 | D4 | semidirect |
| 59. C2×D116 | D4 | semidirect |
| 64. C2×Dic58 | D4 | semidirect |
| 135. #413 | D29 | semidirect |
| 156. C2×M16 | C2×D29 | semidirect |
| 163. #101 | C2×D29 | semidirect |
| 164. #100 | C2×D29 | semidirect |
| 165. C29 | #3021 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271999 | 2 |
| C2×#11745270 | 2 |
| #14271727 | 2 |
| #14271338 | 2 |
| #14271333 | 2 |
| #14271179 | 2 |
| C29×#413 | 2 |
| #3021 | 29 |