Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
454 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 454 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. #14271977 | C2 | semidirect |
| 2. #14271975 | C2 | semidirect |
| 3. #14271965 | C2 | semidirect |
| 4. #14271547 | C2 | semidirect |
| 5. #14271439 | C2 | semidirect |
| 6. #14271434 | C2 | semidirect |
| 7. #14271426 | C2 | semidirect |
| 8. #14271342 | C2 | semidirect |
| 9. #14271337 | C2 | semidirect |
| 10. #14271281 | C2 | semidirect |
| 11. C29×#443 | C2 | semidirect |
| 12. #11745365 | C22 | semidirect |
| 15. C29×#131 | C22 | semidirect |
| 16. #11745313 | C22 | semidirect |
| 27. #11745270 | C22 | semidirect |
| 28. C2×Dic116 | C22 | semidirect |
| 33. C2×#90773 | C22 | semidirect |
| 35. #11745263 | C22 | semidirect |
| 36. #11745237 | C22 | semidirect |
| 37. C29×#108 | C22 | semidirect |
| 38. C29×#104 | C22 | semidirect |
| 39. C4×C8×C29 | C22 | semidirect |
| 40. #11745172 | C22 | semidirect |
| 41. #11745171 | C22 | semidirect |
| 42. #11745167 | C22 | semidirect |
| 44. #11745153 | C22 | semidirect |
| 154. #443 | D29 | semidirect |
| 184. #131 | C2×D29 | semidirect |
| 187. #108 | C2×D29 | semidirect |
| 190. #104 | C2×D29 | semidirect |
| 193. C4×C8 | C2×D29 | semidirect |
| 194. C29 | #3290 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271977 | 2 |
| #14271975 | 2 |
| #14271965 | 2 |
| #14271547 | 2 |
| #14271439 | 2 |
| #14271434 | 2 |
| #14271426 | 2 |
| #14271342 | 2 |
| #14271337 | 2 |
| #14271281 | 2 |
| C29×#443 | 2 |
| #3290 | 29 |