Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
704 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 704 conjugacy classes of subgroups — too many to draw. Only its 145 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 |
|---|---|---|
| 2. C2×#11745271 | C2 | semidirect |
| 3. C2×#11745313 | C2 | semidirect |
| 4. #14271739 | C2 | semidirect |
| 5. #14271347 | C2 | semidirect |
| 6. #14271342 | C2 | semidirect |
| 7. #14271181 | C2 | semidirect |
| 8. #14271145 | C2 | semidirect |
| 9. C29×#421 | C2 | semidirect |
| 23. C22×Dic58 | C22 | semidirect |
| 24. C2×M16×C29 | C22 | semidirect |
| 25. C29×#117 | C22 | semidirect |
| 27. #11745313 | C22 | semidirect |
| 30. C2×#90777 | C22 | semidirect |
| 32. #11745271 | C22 | semidirect |
| 37. #11745237 | C22 | semidirect |
| 38. #11745231 | C22 | semidirect |
| 39. C29×#104 | C22 | semidirect |
| 40. #11745172 | C22 | semidirect |
| 41. #11745171 | C22 | semidirect |
| 42. #11745153 | C22 | semidirect |
| 193. #421 | D29 | semidirect |
| 225. C2×M16 | C2×D29 | semidirect |
| 230. #117 | C2×D29 | semidirect |
| 232. #104 | C2×D29 | semidirect |
| 235. C29 | #3022 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271999 | 2 |
| C2×#11745271 | 2 |
| C2×#11745313 | 2 |
| #14271739 | 2 |
| #14271347 | 2 |
| #14271342 | 2 |
| #14271181 | 2 |
| #14271145 | 2 |
| C29×#421 | 2 |
| #3022 | 29 |