Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
546 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 546 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. #14271818 | C2 | semidirect |
| 3. #14271535 | C2 | semidirect |
| 4. #14271407 | C2 | semidirect |
| 5. #14271368 | C2 | semidirect |
| 6. #14271355 | C2 | semidirect |
| 7. #14271314 | C2 | semidirect |
| 8. #14271306 | C2 | semidirect |
| 9. C4×#90782 | C2 | semidirect |
| 10. #14271241 | C2 | semidirect |
| 11. D42×C29 | C2 | semidirect |
| 14. C2×#90805 | C22 | semidirect |
| 23. C2×#90783 | C22 | semidirect |
| 24. C2×#90783 | C22 | semidirect |
| 27. C2×#90782 | C22 | semidirect |
| 28. #11745286 | C22 | semidirect |
| 29. C2×#90777 | C22 | semidirect |
| 32. C4×D116 | C22 | semidirect |
| 33. #11745231 | C22 | semidirect |
| 35. #11745180 | C22 | semidirect |
| 36. C22⋊#6597 | C22 | semidirect |
| 37. #11745158 | C22 | semidirect |
| 38. #11745157 | C22 | semidirect |
| 39. #11745155 | C22 | semidirect |
| 40. C4⋊#6597 | C22 | semidirect |
| 41. C4×#6597 | C22 | semidirect |
| 73. #90782 | D4 | semidirect |
| 111. D116 | C2×D4 | semidirect |
| 118. #6597 | C2×D4 | semidirect |
| 137. C4×C29 | AGL(1,ℤ/8) | semidirect |
| 144. D42 | D29 | semidirect |
| 190. C29 | #3272 | semidirect |
| 287. C4 | #11745294 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745294 | 2 |
| #14271818 | 2 |
| #14271535 | 2 |
| #14271407 | 2 |
| #14271368 | 2 |
| #14271355 | 2 |
| #14271314 | 2 |
| #14271306 | 2 |
| C4×#90782 | 2 |
| #14271241 | 2 |
| D42×C29 | 2 |
| #3272 | 29 |