Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 141 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. #14271817 | C2 | semidirect |
| 2. #14271509 | C2 | semidirect |
| 3. #14271474 | C2 | semidirect |
| 4. #14271443 | C2 | semidirect |
| 5. #14271397 | C2 | semidirect |
| 6. #14271355 | C2 | semidirect |
| 7. #14271297 | C2 | semidirect |
| 8. C4×#90782 | C2 | semidirect |
| 9. D4×#6597 | C2 | semidirect |
| 10. C2×#11745180 | C2 | semidirect |
| 11. D42×C29 | C2 | semidirect |
| 22. C2×#90782 | C22 | semidirect |
| 23. #11745292 | C22 | semidirect |
| 24. C2×C4⋊Dic29 | C22 | semidirect |
| 25. C22×#6597 | C22 | semidirect |
| 28. C4×D116 | C22 | semidirect |
| 29. #11745231 | C22 | semidirect |
| 32. #11745180 | C22 | semidirect |
| 33. #11745180 | C22 | semidirect |
| 34. #11745180 | C22 | semidirect |
| 35. C22⋊#6597 | C22 | semidirect |
| 36. #11745157 | C22 | semidirect |
| 37. #11745155 | C22 | semidirect |
| 38. #11745155 | C22 | semidirect |
| 39. C4⋊#6597 | C22 | semidirect |
| 40. C4×#6597 | C22 | semidirect |
| 92. D4×C29 | D8 | semidirect |
| 93. D4×C29 | #41 | semidirect |
| 137. D42 | D29 | semidirect |
| 183. C29 | #3294 | semidirect |
| 239. D4 | #90782 | semidirect |
| 240. D4 | #90807 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271817 | 2 |
| #14271509 | 2 |
| #14271474 | 2 |
| #14271443 | 2 |
| #14271397 | 2 |
| #14271355 | 2 |
| #14271297 | 2 |
| C4×#90782 | 2 |
| D4×#6597 | 2 |
| C2×#11745180 | 2 |
| D42×C29 | 2 |
| #3294 | 29 |