Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
784 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 784 conjugacy classes of subgroups — too many to draw. Only its 165 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×#11745311 | C2 | semidirect |
| 2. C22×#90782 | C2 | semidirect |
| 3. #14271727 | C2 | semidirect |
| 4. #14271308 | C2 | semidirect |
| 5. #14271297 | C2 | semidirect |
| 6. #14271168 | C2 | semidirect |
| 7. #14271159 | C2 | semidirect |
| 8. #14271130 | C2 | semidirect |
| 9. C2×C29×H(5,𝔽2) | C2 | semidirect |
| 15. C2×#41×C29 | C22 | semidirect |
| 19. C22×D4×C29 | C22 | semidirect |
| 20. C22×D116 | C22 | semidirect |
| 23. C2×#90784 | C22 | semidirect |
| 27. C2×#90782 | C22 | semidirect |
| 28. C2×#90782 | C22 | semidirect |
| 29. #11745292 | C22 | semidirect |
| 30. #11745288 | C22 | semidirect |
| 31. C2×#90777 | C22 | semidirect |
| 32. C22×#6597 | C22 | semidirect |
| 33. #11745183 | C22 | semidirect |
| 34. #11745180 | C22 | semidirect |
| 35. #11745180 | C22 | semidirect |
| 36. C22⋊#6597 | C22 | semidirect |
| 46. #41×C29 | D4 | semidirect |
| 60. C2×D4×C29 | D4 | semidirect |
| 145. C2×H(5,𝔽2) | D29 | semidirect |
| 166. C2×#41 | C2×D29 | semidirect |
| 171. C22×D4 | C2×D29 | semidirect |
| 188. C29 | #3008 | semidirect |
| 198. #41 | C22⋊D29 | semidirect |
| 217. C2×D4 | C22⋊D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745311 | 2 |
| C22×#90782 | 2 |
| #14271727 | 2 |
| #14271308 | 2 |
| #14271297 | 2 |
| #14271168 | 2 |
| #14271159 | 2 |
| #14271130 | 2 |
| C2×C29×H(5,𝔽2) | 2 |
| #3008 | 29 |