Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
418 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 418 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 |
|---|---|---|
| 2. #14271643 | C2 | semidirect |
| 3. #14271490 | C2 | semidirect |
| 4. #14271489 | C2 | semidirect |
| 5. #14271483 | C2 | semidirect |
| 6. #14271478 | C2 | semidirect |
| 7. #14271206 | C2 | semidirect |
| 8. #14271167 | C2 | semidirect |
| 9. C2×#11745169 | C2 | semidirect |
| 10. #14271129 | C2 | semidirect |
| 11. C29×#427 | C2 | semidirect |
| 21. #11745254 | C22 | semidirect |
| 22. C4⋊C4×D29 | C22 | semidirect |
| 29. C29×#107 | C22 | semidirect |
| 30. C29×#107 | C22 | semidirect |
| 31. C29×#106 | C22 | semidirect |
| 32. C29×#106 | C22 | semidirect |
| 35. #11745168 | C22 | semidirect |
| 36. #11745168 | C22 | semidirect |
| 39. #11745156 | C22 | semidirect |
| 40. #11745155 | C22 | semidirect |
| 136. #427 | D29 | semidirect |
| 164. #107 | C2×D29 | semidirect |
| 165. #107 | C2×D29 | semidirect |
| 167. #106 | C2×D29 | semidirect |
| 168. #106 | C2×D29 | semidirect |
| 175. C29 | #3096 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271732 | 2 |
| #14271643 | 2 |
| #14271490 | 2 |
| #14271489 | 2 |
| #14271483 | 2 |
| #14271478 | 2 |
| #14271206 | 2 |
| #14271167 | 2 |
| C2×#11745169 | 2 |
| #14271129 | 2 |
| C29×#427 | 2 |
| #3096 | 29 |