Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
500 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#11745312 | C2 | semidirect |
| 2. C22×#90772 | C2 | semidirect |
| 3. #14271675 | C2 | semidirect |
| 4. #14271670 | C2 | semidirect |
| 5. #14271420 | C2 | semidirect |
| 6. #14271415 | C2 | semidirect |
| 7. #14271412 | C2 | semidirect |
| 8. #14271408 | C2 | semidirect |
| 9. #14271199 | C2 | semidirect |
| 10. #14271160 | C2 | semidirect |
| 11. C29×#416 | C2 | semidirect |
| 19. C2×#90785 | C22 | semidirect |
| 20. C2×#90784 | C22 | semidirect |
| 24. C2×#90783 | C22 | semidirect |
| 25. C2×#90782 | C22 | semidirect |
| 37. C29×#103 | C22 | semidirect |
| 38. C29×#102 | C22 | semidirect |
| 39. #11745169 | C22 | semidirect |
| 40. #11745164 | C22 | semidirect |
| 41. #11745156 | C22 | semidirect |
| 42. #11745155 | C22 | semidirect |
| 82. C2×#6597 | D4 | semidirect |
| 153. #416 | D29 | semidirect |
| 188. #103 | C2×D29 | semidirect |
| 190. #102 | C2×D29 | semidirect |
| 191. C29 | #3054 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745312 | 2 |
| C22×#90772 | 2 |
| #14271675 | 2 |
| #14271670 | 2 |
| #14271420 | 2 |
| #14271415 | 2 |
| #14271412 | 2 |
| #14271408 | 2 |
| #14271199 | 2 |
| #14271160 | 2 |
| C29×#416 | 2 |
| #3054 | 29 |