Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
476 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 125 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. #14271966 | C2 | semidirect |
| 2. #14271965 | C2 | semidirect |
| 3. #14271538 | C2 | semidirect |
| 4. #14271433 | C2 | semidirect |
| 5. #14271431 | C2 | semidirect |
| 6. #14271430 | C2 | semidirect |
| 7. #14271331 | C2 | semidirect |
| 8. #14271329 | C2 | semidirect |
| 9. #14271280 | C2 | semidirect |
| 10. #14271278 | C2 | semidirect |
| 11. C29×#576 | C2 | semidirect |
| 12. C29×H(5,𝔽2) | C22 | semidirect |
| 13. #11745364 | C22 | semidirect |
| 15. C29×AGL(1,ℤ/8) | C22 | semidirect |
| 19. C2×D8×C29 | C22 | semidirect |
| 20. C29×#131 | C22 | semidirect |
| 24. #11745311 | C22 | semidirect |
| 25. #11745311 | C22 | semidirect |
| 26. #11745310 | C22 | semidirect |
| 27. #11745302 | C22 | semidirect |
| 29. #11745294 | C22 | semidirect |
| 31. C2×#90782 | C22 | semidirect |
| 35. C2×D232 | C22 | semidirect |
| 36. #11745263 | C22 | semidirect |
| 37. #11745185 | C22 | semidirect |
| 38. #11745185 | C22 | semidirect |
| 39. #11745181 | C22 | semidirect |
| 40. #11745173 | C22 | semidirect |
| 41. #11745171 | C22 | semidirect |
| 42. #11745170 | C22 | semidirect |
| 43. #11745167 | C22 | semidirect |
| 44. C8×Dic29 | C22 | semidirect |
| 61. Q16×C29 | D4 | semidirect |
| 63. SD16×C29 | D4 | semidirect |
| 67. D8×C29 | D4 | semidirect |
| 72. #90785 | D4 | semidirect |
| 75. #90784 | D4 | semidirect |
| 77. #90783 | D4 | semidirect |
| 83. #90782 | D4 | semidirect |
| 149. #576 | D29 | semidirect |
| 166. H(5,𝔽2) | C2×D29 | semidirect |
| 174. AGL(1,ℤ/8) | C2×D29 | semidirect |
| 185. C2×D8 | C2×D29 | semidirect |
| 188. #131 | C2×D29 | semidirect |
| 198. C29 | #3292 | semidirect |
| 216. Q16 | C22⋊D29 | semidirect |
| 223. SD16 | C22⋊D29 | semidirect |
| 235. D8 | C22⋊D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271966 | 2 |
| #14271965 | 2 |
| #14271538 | 2 |
| #14271433 | 2 |
| #14271431 | 2 |
| #14271430 | 2 |
| #14271331 | 2 |
| #14271329 | 2 |
| #14271280 | 2 |
| #14271278 | 2 |
| C29×#576 | 2 |
| #3292 | 29 |