Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
492 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 127 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. #14271711 | C2 | semidirect |
| 2. C4×D4×D29 | C2 | semidirect |
| 3. #14271475 | C2 | semidirect |
| 4. #14271444 | C2 | semidirect |
| 5. #14271443 | C2 | semidirect |
| 6. #14271355 | C2 | semidirect |
| 7. #14271295 | C2 | semidirect |
| 8. D8×Dic29 | C2 | semidirect |
| 9. #14271243 | C2 | semidirect |
| 10. #14271215 | C2 | semidirect |
| 11. C29×#459 | C2 | semidirect |
| 16. C29×#127 | C22 | semidirect |
| 23. D4×Dic29 | C22 | semidirect |
| 32. #11745231 | C22 | semidirect |
| 33. C29×C4⋊C8 | C22 | semidirect |
| 34. C29×#102 | C22 | semidirect |
| 36. #11745180 | C22 | semidirect |
| 39. #11745166 | C22 | semidirect |
| 40. C8×Dic29 | C22 | semidirect |
| 41. #11745155 | C22 | semidirect |
| 42. C4⋊#6597 | C22 | semidirect |
| 96. D4×C29 | #41 | semidirect |
| 112. D116 | #41 | semidirect |
| 119. C4×D29 | D8 | semidirect |
| 154. #459 | D29 | semidirect |
| 172. #127 | C2×D29 | semidirect |
| 190. C4⋊C8 | C2×D29 | semidirect |
| 194. #102 | C2×D29 | semidirect |
| 197. C29 | #3100 | semidirect |
| 256. D4 | #90807 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271711 | 2 |
| C4×D4×D29 | 2 |
| #14271475 | 2 |
| #14271444 | 2 |
| #14271443 | 2 |
| #14271355 | 2 |
| #14271295 | 2 |
| D8×Dic29 | 2 |
| #14271243 | 2 |
| #14271215 | 2 |
| C29×#459 | 2 |
| #3100 | 29 |