Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
492 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 492 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. #14271708 | C2 | semidirect |
| 2. C2×#11745255 | C2 | semidirect |
| 3. #14271476 | C2 | semidirect |
| 4. #14271442 | C2 | semidirect |
| 5. #14271357 | C2 | semidirect |
| 6. #14271299 | C2 | semidirect |
| 7. #14271296 | C2 | semidirect |
| 8. #14271245 | C2 | semidirect |
| 9. #14271243 | C2 | semidirect |
| 10. #14271213 | C2 | semidirect |
| 11. C29×#480 | C2 | semidirect |
| 17. #11745302 | C22 | semidirect |
| 19. D4×Dic29 | C22 | semidirect |
| 29. #11745255 | C22 | semidirect |
| 30. #11745250 | C22 | semidirect |
| 33. C29×#107 | C22 | semidirect |
| 34. C29×#102 | C22 | semidirect |
| 38. #11745162 | C22 | semidirect |
| 39. C8×Dic29 | C22 | semidirect |
| 41. #11745157 | C22 | semidirect |
| 42. #11745155 | C22 | semidirect |
| 104. C2×Dic29 | D8 | semidirect |
| 112. D116 | #41 | semidirect |
| 146. #480 | D29 | semidirect |
| 183. #107 | C2×D29 | semidirect |
| 188. #102 | C2×D29 | semidirect |
| 192. C29 | #3100 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271708 | 2 |
| C2×#11745255 | 2 |
| #14271476 | 2 |
| #14271442 | 2 |
| #14271357 | 2 |
| #14271299 | 2 |
| #14271296 | 2 |
| #14271245 | 2 |
| #14271243 | 2 |
| #14271213 | 2 |
| C29×#480 | 2 |
| #3100 | 29 |