Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
548 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 135 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×M16×D29 | C2 | semidirect |
| 3. #14271675 | C2 | semidirect |
| 4. C2×#11745300 | C2 | semidirect |
| 5. #14271415 | C2 | semidirect |
| 6. #14271408 | C2 | semidirect |
| 7. #14271398 | C2 | semidirect |
| 8. #14271391 | C2 | semidirect |
| 9. #14271206 | C2 | semidirect |
| 10. #14271165 | C2 | semidirect |
| 11. C29×#418 | C2 | semidirect |
| 23. C2×#90783 | C22 | semidirect |
| 25. C2×#90782 | C22 | semidirect |
| 29. C2×#90772 | C22 | semidirect |
| 30. C2×C8×D29 | C22 | semidirect |
| 31. #11745259 | C22 | semidirect |
| 32. #11745259 | C22 | semidirect |
| 33. #11745257 | C22 | semidirect |
| 34. #11745257 | C22 | semidirect |
| 39. C29×#102 | C22 | semidirect |
| 40. C29×#102 | C22 | semidirect |
| 41. #11745169 | C22 | semidirect |
| 42. #11745164 | C22 | semidirect |
| 43. #11745156 | C22 | semidirect |
| 44. #11745155 | C22 | semidirect |
| 89. #90777 | D4 | semidirect |
| 136. #6597 | C2×D4 | semidirect |
| 155. C2×D29 | AGL(1,ℤ/8) | semidirect |
| 174. #418 | D29 | semidirect |
| 215. #102 | C2×D29 | semidirect |
| 216. #102 | C2×D29 | semidirect |
| 217. C29 | #3055 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745294 | 2 |
| C2×M16×D29 | 2 |
| #14271675 | 2 |
| C2×#11745300 | 2 |
| #14271415 | 2 |
| #14271408 | 2 |
| #14271398 | 2 |
| #14271391 | 2 |
| #14271206 | 2 |
| #14271165 | 2 |
| C29×#418 | 2 |
| #3055 | 29 |