Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
476 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 117 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. #14271968 | C2 | semidirect |
| 2. #14271967 | C2 | semidirect |
| 3. #14271964 | C2 | semidirect |
| 4. #14271538 | C2 | semidirect |
| 5. #14271434 | C2 | semidirect |
| 6. #14271432 | C2 | semidirect |
| 7. #14271333 | C2 | semidirect |
| 8. #14271329 | C2 | semidirect |
| 9. #14271279 | C2 | semidirect |
| 10. #14271278 | C2 | semidirect |
| 11. C29×#472 | C2 | semidirect |
| 12. #11745364 | C22 | semidirect |
| 13. #11745359 | C22 | semidirect |
| 14. C29×AGL(1,ℤ/8) | C22 | semidirect |
| 15. C2×D8×C29 | C22 | semidirect |
| 16. C29×#131 | C22 | semidirect |
| 18. #11745302 | C22 | semidirect |
| 19. #11745294 | C22 | semidirect |
| 20. C2×#90782 | C22 | semidirect |
| 29. #11745270 | C22 | semidirect |
| 30. #11745270 | C22 | semidirect |
| 31. #11745269 | C22 | semidirect |
| 35. C2×D232 | C22 | semidirect |
| 36. #11745263 | C22 | semidirect |
| 37. C29×#108 | C22 | semidirect |
| 38. C29×#100 | C22 | semidirect |
| 39. #11745185 | C22 | semidirect |
| 40. #11745173 | C22 | semidirect |
| 41. #11745173 | C22 | semidirect |
| 42. #11745171 | C22 | semidirect |
| 43. #11745170 | C22 | semidirect |
| 44. C8×Dic29 | C22 | semidirect |
| 70. #90785 | D4 | semidirect |
| 71. #90784 | D4 | semidirect |
| 73. #90783 | D4 | semidirect |
| 77. #90782 | D4 | semidirect |
| 81. Dic116 | D4 | semidirect |
| 86. D232 | D4 | semidirect |
| 89. #90773 | D4 | semidirect |
| 153. #472 | D29 | semidirect |
| 174. AGL(1,ℤ/8) | C2×D29 | semidirect |
| 185. C2×D8 | C2×D29 | semidirect |
| 188. #131 | C2×D29 | semidirect |
| 191. #108 | C2×D29 | semidirect |
| 196. #100 | C2×D29 | semidirect |
| 198. C29 | #3292 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271968 | 2 |
| #14271967 | 2 |
| #14271964 | 2 |
| #14271538 | 2 |
| #14271434 | 2 |
| #14271432 | 2 |
| #14271333 | 2 |
| #14271329 | 2 |
| #14271279 | 2 |
| #14271278 | 2 |
| C29×#472 | 2 |
| #3292 | 29 |