Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
994 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 994 conjugacy classes of subgroups — too many to draw. Only its 143 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. C22×D4×D29 | C2 | semidirect |
| 2. C2×#11745273 | C2 | semidirect |
| 3. #14271673 | C2 | semidirect |
| 4. #14271316 | C2 | semidirect |
| 5. #14271315 | C2 | semidirect |
| 6. #14271314 | C2 | semidirect |
| 7. #14271296 | C2 | semidirect |
| 8. #14271295 | C2 | semidirect |
| 9. #14271166 | C2 | semidirect |
| 10. #14271125 | C2 | semidirect |
| 11. C29×#447 | C2 | semidirect |
| 15. C2×#90807 | C22 | semidirect |
| 23. C2×D8×C29 | C22 | semidirect |
| 24. C29×#121 | C22 | semidirect |
| 25. #11745300 | C22 | semidirect |
| 28. C2×#90783 | C22 | semidirect |
| 29. C2×#90782 | C22 | semidirect |
| 30. #11745286 | C22 | semidirect |
| 32. C2×#90773 | C22 | semidirect |
| 33. C2×#90772 | C22 | semidirect |
| 34. #11745259 | C22 | semidirect |
| 35. #11745254 | C22 | semidirect |
| 38. C29×#102 | C22 | semidirect |
| 39. C29×C22⋊C8 | C22 | semidirect |
| 40. #11745180 | C22 | semidirect |
| 41. C22⋊#6597 | C22 | semidirect |
| 42. #11745169 | C22 | semidirect |
| 43. #11745168 | C22 | semidirect |
| 44. #11745157 | C22 | semidirect |
| 57. C2×D4×C29 | C23 | semidirect |
| 72. D4×D29 | D4 | semidirect |
| 81. C2×Dic58 | C23 | semidirect |
| 83. C2×C8×C29 | C23 | semidirect |
| 84. C4⋊C4×C29 | C23 | semidirect |
| 93. C4⋊Dic29 | C23 | semidirect |
| 96. C2×#6597 | C23 | semidirect |
| 160. C22×C29 | AGL(1,ℤ/8) | semidirect |
| 174. C2×D29 | AGL(1,ℤ/8) | semidirect |
| 190. #447 | D29 | semidirect |
| 217. C2×D8 | C2×D29 | semidirect |
| 223. #121 | C2×D29 | semidirect |
| 231. #102 | C2×D29 | semidirect |
| 234. C22⋊C8 | C2×D29 | semidirect |
| 235. C29 | #3003 | semidirect |
| 264. C2×D4 | C22×D29 | semidirect |
| 279. C2×C8 | C22×D29 | semidirect |
| 283. C4⋊C4 | C22×D29 | semidirect |
| 363. C22 | #11745273 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D4×D29 | 2 |
| C2×#11745273 | 2 |
| #14271673 | 2 |
| #14271316 | 2 |
| #14271315 | 2 |
| #14271314 | 2 |
| #14271296 | 2 |
| #14271295 | 2 |
| #14271166 | 2 |
| #14271125 | 2 |
| C29×#447 | 2 |
| #3003 | 29 |