Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 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×#11745294 | C2 | semidirect |
| 2. C2×#11745263 | C2 | semidirect |
| 3. #14271744 | C2 | semidirect |
| 4. #14271730 | C2 | semidirect |
| 5. #14271415 | C2 | semidirect |
| 6. #14271408 | C2 | semidirect |
| 7. #14271398 | C2 | semidirect |
| 8. #14271391 | C2 | semidirect |
| 9. #14271203 | C2 | semidirect |
| 10. #14271160 | C2 | semidirect |
| 11. C2×C29×#102 | C2 | semidirect |
| 29. C2×#90772 | C22 | semidirect |
| 30. C2×C8×D29 | C22 | semidirect |
| 32. #11745259 | C22 | semidirect |
| 34. #11745257 | C22 | semidirect |
| 37. #11745169 | C22 | semidirect |
| 38. #11745169 | C22 | semidirect |
| 39. #11745164 | C22 | semidirect |
| 40. #11745164 | C22 | semidirect |
| 41. #11745156 | C22 | semidirect |
| 42. #11745155 | C22 | semidirect |
| 81. #90777 | D4 | semidirect |
| 155. C2×#102 | D29 | semidirect |
| 194. C29 | #3062 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745294 | 2 |
| C2×#11745263 | 2 |
| #14271744 | 2 |
| #14271730 | 2 |
| #14271415 | 2 |
| #14271408 | 2 |
| #14271398 | 2 |
| #14271391 | 2 |
| #14271203 | 2 |
| #14271160 | 2 |
| C2×C29×#102 | 2 |
| #3062 | 29 |