Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
410 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 410 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 |
|---|---|---|
| 3. #14271507 | C2 | semidirect |
| 4. #14271506 | C2 | semidirect |
| 5. #14271500 | C2 | semidirect |
| 6. #14271495 | C2 | semidirect |
| 7. #14271203 | C2 | semidirect |
| 8. #14271173 | C2 | semidirect |
| 9. #14271171 | C2 | semidirect |
| 11. C29×#428 | C2 | semidirect |
| 33. C29×#107 | C22 | semidirect |
| 34. C29×#106 | C22 | semidirect |
| 37. #11745164 | C22 | semidirect |
| 38. #11745164 | C22 | semidirect |
| 39. #11745158 | C22 | semidirect |
| 40. #11745158 | C22 | semidirect |
| 41. #11745156 | C22 | semidirect |
| 42. #11745155 | C22 | semidirect |
| 148. #428 | D29 | semidirect |
| 180. #107 | C2×D29 | semidirect |
| 182. #106 | C2×D29 | semidirect |
| 189. C29 | #3095 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745259 | 2 |
| #117×D29 | 2 |
| #14271507 | 2 |
| #14271506 | 2 |
| #14271500 | 2 |
| #14271495 | 2 |
| #14271203 | 2 |
| #14271173 | 2 |
| #14271171 | 2 |
| #14271126 | 2 |
| C29×#428 | 2 |
| #3095 | 29 |